Answer Key 10.7

[latexpage]

1. \(\begin{array}{rrrrrrrrrrl}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   x&+&y&=&22&\Rightarrow &x&=&22&-&y \\
   x&-&y&=&120&&&&&& \\ \\
   (22&-&y)y&=&120&&&&&& \\
   22y&-&y^2&=&120&&&&&& \\ \\
   &&0&=&y^2&-&22y&+&120&& \\
   &&0&=&y^2&-&12y&-&10y&+&120 \\
   \midrule
   &&0&=&y(y&-&12)&-&10(y&-&12) \\
   &&0&=&(y&-&12)(y&-&10)&& \\ \\
   &&y&=&12,&10&&&&&
   \end{array}\)

   \(\therefore \text{ numbers are }10, 12\)

2. \(\begin{array}{rrrrccrrrrrrrrl}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   &&&&x&-&y&=&4&\Rightarrow &x&=&y&+&4 \\
   &&&&x&\cdot &y&=&140&&&&&& \\ \\
   &&&&(y&+&4)y&=&140&&&&&& \\
   &&&&y^2&+&4y&=&140&&&&&& \\ \\
   &&y^2&+&4y&-&140&=&0&&&&&& \\
   y^2&-&10y&+&14y&-&140&=&0&&&&&& \\
   \midrule
   y(y&-&10)&+&14(y&-&10)&=&0&&&&&& \\
   &&(y&-&10)(y&+&14)&=&0&&&&&& \\ \\
   &&&&&&y&=&10,&-14&&&&& \\ \\
   &&&&&&y&=&10,&x&=&10&+&4&= 14 \\
   &&&&&&y&=&-14,&x&=&-14&+&4&= -10 \\
   \end{array}\)

   \(\therefore \text{ numbers are }10, 14\text{ and }-10, -14\)

3. \(\begin{array}{rrrrcrrrrrrrrrl}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   &&&&A&-&B&=&8&\Rightarrow &A&=&B&+&8 \\
   &&&&A^2&+&B^2&=&320&&&&&& \\ \\
   &&(B&+&8)^2&+&B^2&=&320&&&&&& \\
   B^2&+&16B&+&64&+&B^2&=&320&&&&&& \\
   &&&-&320&&&&-320&&&&&& \\
   \midrule
   &&2B^2&+&16B&-&256&=&0&&&&&& \\
   &&2(B^2&+&8B&-&128)&=&0&&&&&& \\
   &&2(B&+&16)(B&-&8)&=&0&&&&&& \\ \\
   &&&&&&B&=&-16,&8&&&&& \\ \\
   &&&&&&\therefore A&=&B&+&8&&&& \\
   &&&&&&A&=&-8,&16&&&&&
   \end{array}\)

   \(\therefore (-16, -8)\text{ and }(8,16)\)

4. \(\begin{array}{rrrrcrrrrrrrrr}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   x, &x&+&2&&&&&&&&&& \\ \\
   &&x^2&+&(x&+&2)^2&=&244&&&&& \\
   x^2&+&x^2&+&4x&+&4&=&244&&&&& \\
   &&&&&&-244&&-244&&&&& \\
   \midrule
   &&2x^2&+&4x&-&240&=&0&&&&& \\
   &&2(x^2&+&2x&-&120)&=&0&&&&& \\
   &&2(x&-&10)(x&+&12)&=&0&&&&& \\ \\
   &&&&&&x&=&10, &-12&&&& \\ \\
   &&&&&&x&=&10, &x&+&2&=&12 \\
   &&&&&&x&=&-12, &x&+&2&=&-10
   \end{array}\)

   \(\therefore \text{ numbers are }10, 12\text{ or }-12, -10\)

5. \(\begin{array}{rrrrrrrrrrrr}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   x,&x&+&2&&&&&&&& \\ \\
   &&x^2&-&(x&+&2)^2&=&60&&& \\
   x^2&-&(x^2&+&4x&+&4)&=&60&&& \\
   x^2&-&x^2&-&4x&-&4&=&60&&& \\
   &&&&&+&4&&+4&&& \\
   \midrule
   &&&&&&\dfrac{-4x}{-4}&=&\dfrac{64}{-4}&&& \\ \\
   &&&&&&x&=&-16&&& \\ \\
   &&&&x&+&2&\Rightarrow &-16&+&2& \\
   &&&&&&&\Rightarrow &-14&&& \\
   \end{array}\)

   \(-16, -14\)

6. \(\begin{array}{rrrrcrrrl}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   x,&x&+&2&&&&& \\ \\
   &&x^2&+&(x&+&2)^2&=&\phantom{-}452 \\
   x^2&+&x^2&+&4x&+&4&=&\phantom{-}452 \\
   &&&&&-&452&&-452 \\
   \midrule
   &&2x^2&+&4x&-&448&=&0 \\
   &&2(x^2&+&2x&-&224)&=&0 \\
   &&2(x&-&14)(x&+&16)&=&0 \\ \\
   &&&&&&x&=&14, -16 \\ \\
   &&&&&&x&=&14 \\
   &&&&x&+&2&=&16 \\ \\
   &&&&&&x&=&-16 \\
   &&&&x&+&2&=&-14
   \end{array}\)

   \(14,16\text{ and }-16,-14\)

7. \(\begin{array}{rrcrrrrrrrr}
   \\ \\ \\ \\ \\ \\ \\
   x,&x&+&2,&x&+&4&&&& \\ \\
   &&x(x&+&2)&=&38&+&x&+&4 \\
   x^2&+&2x&&&=&42&+&x&& \\
   &-&x&-&42&&-42&-&x&& \\
   \midrule
   x^2&+&x&-&42&=&0&&&& \\
   (x&+&7)(x&-&6)&=&0&&&& \\
   &&&&x&=&\cancel{-7},&6&&& \\
   \end{array}\)

   \(\therefore \text{ numbers are }6,8,10\)

8. \(x, x+2, x+4\)\(\begin{array}{rrrrrrrrrrr}
   \\ \\ \\ \\ \\ \\ \\ \\ \\
   &&(x)(x&+&2)&=&52&+&x&+&4 \\ \\
   x^2&+&2x&&&=&56&+&x&& \\
   &-&x&-&56&&-56&-&x&& \\
   \midrule
   x^2&+&x&-&56&=&0&&&& \\
   (x&+&8)(x&-&7)&=&0&&&& \\ \\
   &&&&x&=&\cancel{-8}, 7&&&&
   \end{array}\)

   \(\therefore \text{ numbers are }7,9,11\)

9. \(\begin{array}{rrrrrrrrlrrr}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   &&A&=&T&+&4&&&&& \\ \\
   A&\cdot &T&=&80&+&(A&-&4)&(T&-&4) \\
   (T&+&4)T&=&80&+&(T&+&\cancel{4-4})&(T&-&4) \\ \\
   T^2&+&4T&=&80&+&T^2&-&4T&&& \\
   -T^2&+&4T&&&-&T^2&+&4T&&& \\
   \midrule
   &&\dfrac{8T}{8}&=&\dfrac{80}{8}&&&&&&& \\ \\
   &&T&=&10&&&&&&& \\ \\
   &&\therefore A&=&T&+&4&&&&& \\
   &&A&=&10&+&4&=&14&&&
   \end{array}\)
10. \(\begin{array}{rrcrrrcrcrrrr}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&C&=&K&+&3&&&&&& \\
    &&CK&=&(C&+&5)&&(K&+&5)&-&130 \\ \\
    (K&+&3)K&=&(K&+&3&+&5)(K&+&5)&-&130 \\
    K^2&+&3K&=&K^2&+&13K&+&40&-&130&& \\
    -K^2&-&13K&&-K^2&-&13K&&&&&& \\
    \midrule
    &&\dfrac{-10K}{-10}&=&\dfrac{-90}{-10}&&&&&&&& \\ \\
    &&K&=&9&&&&&&&& \\ \\
    &&\therefore C&=&9&+&3&=&12&&&&
    \end{array}\)
11. \(\begin{array}{rrrrcrrrrrrrr}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&&&J&=&S&+&1&& \\ \\
    &&(J&+&5)(S&+&5)&=&230&+&J&\cdot &S \\
    (S&+&1&+&5)(S&+&5)&=&230&+&(S&+&1)S \\
    &&(S&+&6)(S&+&5)&=&230&+&S^2&+&S \\ \\
    &&S^2&+&11S&+&30&=&S^2&+&S&+&230 \\
    &&-S^2&-&S&-&30&&-S^2&-&S&-&30 \\
    \midrule
    &&&&&&\dfrac{10S}{10}&=&\dfrac{200}{10}&&&& \\ \\
    &&&&&&S&=&20&&&& \\
    &&&&&&J&=&21&&&&
    \end{array}\)
12. \(\begin{array}{rrcrcrrrrrrrr}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&&&J&=&S&+&2&& \\
    &&(S&+&2)(J&+&2)&=&48&+&S&\cdot &J \\ \\
    (S&+&2)(S&+&2&+&2)&=&48&+&S(S&+&2) \\
    &&(S&+&2)(S&+&4)&=&48&+&S^2&+&25 \\ \\
    &&S^2&+&6S&+&8&=&48&+&S^2&+&25 \\
    &&-S^2&-&2S&-&8&&-8&-&S^2&-&25 \\
    \midrule
    &&&&&&\dfrac{4S}{4}&=&\dfrac{40}{4}&&&& \\ \\
    &&&&&&S&=&10&&&& \\
    &&&&&&J&=&12&&&&
    \end{array}\)
13. \(\begin{array}{ll}
    \\ \\ \\
    \begin{array}{rrrrrrrrl}
    \\ \\ \\ \\ \\ \\ \\
    &&&&&&d&=&r\cdot t \\ \\
    &&&&r&\cdot &t&=&240\ \\
    &&&&&&\therefore r&=&\dfrac{240}{t} \\ \\
    &&(r&+&20)(t&-&1)&=&240 \\
    &&(\dfrac{240}{t}&+&20)(t&-&1)&=&240 \\ \\
    \cancel{240}&+&20t&-&\dfrac{240}{t}&-&20&=&\cancel{240} \\ \\
    &&(20t&-&\dfrac{240}{t}&-&20&=&0)(t) \\ \\
    &&(20t^2&-&240&-&20t&=&0)(\div 20)
    \end{array}
    &\hspace{0.25in}
    \begin{array}{rrcrcrl}
    t^2&-&12&-&t&=&0 \\
    (t&-&4)(t&+&3)&=&0 \\ \\
    &&&&t&=&4, \cancel{-3} \\ \\
    &&&&r&=&\dfrac{240}{4}\text{ or }60\text{ km/h} \\ \\
    &&&&\text{faster}&=&80\text{ km/h}
    \end{array}
    \end{array}\)
14. \(\begin{array}{ll}
    \begin{array}{rrrrrrrrl}
    \\ \\ \\ \\ \\ \\ \\
    &&&&&&d&=&r\cdot t \\
    &&&&r&\cdot &t&=&100 \\
    &&&&&&r&=&\dfrac{100}{t} \\ \\
    &&(r&+&20)(t&-&0.5)&=&120 \\
    &&(\dfrac{100}{t}&+&20)(t&-&0.5)&=&120 \\
    100&+&20t&-&\dfrac{50}{t}&-&10&=&120 \\
    &&&&&-&120&&-120 \\
    \midrule
    &&20t&-&30&-&\dfrac{50}{t}&=&0 \\ \\
    &&(20t&-&30&-&\dfrac{50}{t}&=&0)(t) \\ \\
    &&(20t^2&-&30t&-&50&=&0)(\div 10)
    \end{array}
    &\hspace{0.25in}
    \begin{array}{rrrrrrl}
    2t^2&-&3t&-&5&=&0 \\
    &&&&t&=&\dfrac{-(-3)\pm \sqrt{(-3)^2-4(2)(-5)}}{2(2)} \\ \\
    &&&&t&=&\dfrac{3\pm 7}{4}=\dfrac{10}{4}\text{ or }\cancel{\dfrac{-4}{4}} \\ \\
    &&&&t&=&2.5\text{ h}
    \end{array}
    \end{array}\)

    \(\text{Answer: }\dfrac{100\text{ km}}{2.5\text{ h}}=\dfrac{40\text{ km}}{\text{h}}, \dfrac{120\text{ km}}{2\text{ h}}=\dfrac{60\text{ km}}{\text{h}}\)

15. \(\begin{array}{ll}
    \\ \\ \\ \\
    \begin{array}{rrrrrrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\
    &&&&&&d&=&r\cdot t \\
    &&&&r&\cdot &t&=&150 \\
    &&&&&&r&=&\dfrac{150}{t} \\ \\
    &&(r&+&5)(t&-&1.5)&=&150 \\
    &&(\dfrac{150}{t}&+&5)(t&-&1.5)&=&150 \\ \\
    \cancel{150}&+&5t&-&\dfrac{225}{t}&-&7.5&=&\cancel{150} \\ \\
    &&(5t&-&\dfrac{225}{t}&-&7.5&=&0)(t) \\ \\
    &&(5t^2&-&7.5t&-&225&=&0)(2) \\
    &&(10t^2&-&15t&-&450&=&0)(\div 5)
    \end{array}
    &\hspace{0.25in}
    \begin{array}{rrrrrrl}
    \\ \\ \\ \\ \\ \\
    2t^2&-&3t&-&90&=&0 \\
    (t&+&6)(2t&-&15)&=&0 \\
    &&&&t&=&\cancel{-6}, \dfrac{15}{2} \\ \\
    &&&&r&=&\dfrac{150}{t} \\ \\
    &&&&r&=&\dfrac{150}{\dfrac{15}{2}} \\ \\
    &&&&r&=&\dfrac{150}{1}\cdot \dfrac{2}{15} \\ \\
    &&&&r&=&20\text{ km/h}
    \end{array}
    \end{array}\)
16. \(\begin{array}{rrrrrrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&&&d&=&r\cdot t \\
    &&&&r&\cdot &t&=&180\Rightarrow r=\dfrac{180}{t} \\ \\
    &&(r&+&15)(t&-&1)&=&180 \\
    &&(\dfrac{180}{t}&+&15)(t&-&1)&=&180 \\ \\
    \cancel{180}&+&15t&-&\dfrac{180}{t}&-&15&=&\cancel{180} \\
    &&(15t&-&15&-&\dfrac{180}{t}&=&0)(t) \\
    &&(15t^2&-&15t&-&180&=&0)(\div 15) \\ \\
    &&t^2&-&t&-&12&=&0 \\
    &&(t&-&4)(t&+&3)&=&0 \\
    &&&&&&t&=&4, \cancel{-3} \\ \\
    &&&&&&r&=&\dfrac{180}{4}=45
    \end{array}\)
17. \(\begin{array}{rrrrcrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&r&\cdot &t&=&72\Rightarrow r=\dfrac{72}{t} \\ \\
    &&(r&+&12)(9&-&t)&=&72 \\ \\
    &&(\dfrac{72}{t}&+&12)(9&-&t)&=&72 \\
    \dfrac{648}{t}&+&108&-&72&-&12t&=&72 \\
    &&&-&72&&&&-72 \\
    \midrule
    &&(-12t&-&36&+&\dfrac{648}{t}&=&0)(t) \\ \\
    &&(-12t^2&-&36t&+&648&=&0)(\div -12) \\ \\
    &&t^2&+&3t&-&54&=&0 \\
    &&(t&+&9)(t&-&6)&=&0 \\
    &&&&&&t&=&\cancel{-9}, 6 \\ \\
    &&&&&&r&=&\dfrac{72}{6}=12\text{ (there)} \\ \\
    &&&&&&r&=&24\text{ (return)}
    \end{array}\)
18. \(\begin{array}{rrrrcrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&r&\cdot &t&=&120\Rightarrow r=\dfrac{120}{t} \\
    &&(r&+&10)(7&-&t)&=&120 \\ \\
    &&(\dfrac{120}{t}&+&10)(7&-&t)&=&120 \\
    \dfrac{840}{t}&+&70&-&120&-&10t&=&120 \\
    &&&-&120&&&&-120 \\
    \midrule
    &&(-10t&-&170&+&\dfrac{840}{t}&=&0)(t) \\
    &&(-10t^2&-&170t&+&840&=&0)(\div -10) \\ \\
    &&t^2&+&17t&-&84&=&0 \\
    &&(t&+&21)(t&-&4)&=&0 \\
    &&&&&&t&=&\cancel{-21}, 4 \\ \\
    &&&&&&r&=&\dfrac{120}{4}\text{ or }30\text{ km/h} \\ \\
    &&&&r&+&10&=&40\text{ km/h} \\
    \end{array}\)
19. \(\begin{array}{rrrrcrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&r&\cdot &t&=&240\Rightarrow r=\dfrac{240}{t} \\ \\
    &&(r&+&20)(t&-&1)&=&240 \\
    &&(\dfrac{240}{t}&+&20)(t&-&1)&=&240 \\
    \cancel{240}&+&20t&-&\dfrac{240}{t}&-&20&=&\cancel{240} \\ \\
    &&(20t&-&20&-&\dfrac{240}{t}&=&0)(t) \\
    &&(20t^2&-&20t&-&240&=&0)(\div 20) \\ \\
    &&t^2&-&t&-&12&=&0 \\
    &&(t&-&4)(t&+&3)&=&0 \\
    &&&&&&t&=&4, \cancel{-3} \\ \\
    &&&&&&r&=&\dfrac{240}{4}\text{ or }60\text{ km/h}
    \end{array}\)
20. \(\begin{array}{rrrrcrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&r&\cdot &t&=&600\Rightarrow r=\dfrac{600}{t} \\ \\
    &&(r&-&50)(7&-&t)&=&600 \\
    &&(\dfrac{600}{t}&-&50)(7&-&t)&=&600 \\
    \dfrac{4200}{t}&-&350&-&600&+&50t&=&600 \\
    &&&-&600&&&&-600 \\
    \midrule
    &&(50t&-&1550&+&\dfrac{4200}{t}&=&0)(t) \\
    &&(50t^2&-&1550t&+&4200&=&0)(\div 50) \\ \\
    &&t^2&-&31t&+&84&=&0 \\
    &&(t&-&3)(t&-&28)&=&0 \\
    &&&&&&t&=&3, \cancel{28} \\ \\
    &&&&&&r&=&\dfrac{600}{3}\text{ or }200\text{ km/h}
    \end{array}\)
21. \(\begin{array}{rrrrlrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    L&=&4&+&W&&&& \\
    \text{Area}&=&L&\cdot &W&&&& \\ \\
    60&=&(4&+&W)W&&&& \\
    60&=&4W&+&W^2&&&& \\ \\
    0&=&W^2&+&4W&-&60&& \\
    0&=&W^2&+&10W&-&6W&-&60 \\
    \midrule
    0&=&W(W&+&10)&-&6(W&+&10) \\
    0&=&(W&+&10)(W&-&6)&& \\ \\
    W&=&\cancel{-10},&6&&&&& \\
    L&=&6&+&4&=&10&&
    \end{array}\)
22. \(\begin{array}{rrrrcrrrr}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    W&=&L&-&10&&&& \\
    \text{Area}&=&L&\cdot &W&&&& \\ \\
    200&=&L(L&-&10)&&&& \\
    200&=&L^2&-&10L&&&& \\ \\
    0&=&L^2&-&10L&-&200&& \\
    0&=&L^2&+&10L&-&20L&-&200 \\
    \midrule
    0&=&L(L&+&10)&-&20(L&+&10) \\
    0&=&(L&+&10)(L&-&20)&& \\ \\
    L&=&\cancel{-10},&20&&&&& \\
    W&=&20&-&10&=&10&&
    \end{array}\)
23. \(\begin{array}{rrrrcrcrcrl}
    \\ \\ \\ \\ \\ \\ \\ \\
    &&&&&&\text{Area}_{\text{large}}&-&\text{Area}_{\text{small}}&=&2800\text{ m}^2 \\ \\
    &&(150&+&2x)(120&+&2x)&-&(150)(120)&=&2800 \\
    \cancel{18000}&+&240x&+&300x&+&4x^2&-&\cancel{18000}&=&2800 \\
    &&&&&&&-&2800&&-2800 \\
    \midrule
    &&&&4x^2&+&540x&-&2800&=&0 \\
    &&&&x^2&+&135x&-&700&=&0 \\
    &&&&(x&-&5)(x&+&140)&=&0 \\
    &&&&&&&&x&=&5, \cancel{-140}
    \end{array}\)

    \(\text{walkway}=5\text{ m}\)

24. \(\begin{array}{rrrrcrcrcrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&&&\text{Area}_{\text{large}}&-&\text{Area}_{\text{small}}&=&74\text{ m}^2 \\ \\
    &&(25&+&2x)(10&+&2x)&-&(25)(10)&=&74 \\
    \cancel{250}&+&20x&+&50x&+&4x^2&-&\cancel{250}&=&74 \\
    &&&&&&&-&74&&-74 \\
    \midrule
    &&&&4x^2&+&70x&-&74&=&0 \\
    &&&&2x^2&+&35x&-&37&=&0 \\
    &&&&(x&-&1)(2x&+&37)&=&0 \\
    &&&&&&&&x&=&1, \cancel{-\dfrac{37}{2}} \\
    \end{array}\)

    \(\text{the overlap}=1\text{ m}\)

25. \(\begin{array}{rrrrrrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&L&=&W&+&4 \\
    &&L&\cdot &W&=&60&& \\ \\
    &&(W&+&4)W&=&60&& \\
    W^2&+&4W&&&=&60&& \\
    &&&-&60&&-60&& \\
    \midrule
    W^2&+&4W&-&60&=&0&& \\
    (W&-&6)(W&+&10)&=&0&& \\ \\
    &&&&W&=&6,&\cancel{-10}& \\
    &&&&L&=&6&+&4=10
    \end{array}\)
26. \(\begin{array}{rrrrrrrrcrr}
    \\ \\ \\ \\ \\ \\ \\
    &&(x&+&5)^2&=&4(x)^2&&&& \\ \\
    x^2&+&10x&+&25&=&4x^2&&&& \\
    -x^2&-&10x&-&25&&-x^2&-&10x&-&25 \\
    \midrule
    &&&&0&=&3x^2&-&10x&-&25 \\
    &&&&0&=&(x&-&5)(3x&+&5) \\
    &&&&x&=&5, &\cancel{-\dfrac{5}{3}}&&&
    \end{array}\)
27. \(\begin{array}{rrrrrrlll}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&L&=&20&+&W \\
    &&L&\cdot &W&=&2400&& \\ \\
    &&(20&+&W)W&=&2400&& \\
    W^2&+&20W&&&=&2400&& \\
    &&&-&2400&&-2400&& \\
    \midrule
    W^2&+&20W&-&2400&=&0&& \\
    (W&+&60)(W&-&40)&=&0&& \\ \\
    &&&&W&=&\cancel{-60},&40& \\
    &&&&L&=&20&+&40=60
    \end{array}\)
28. \(\begin{array}{rrrrcrrrrrrrr}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &&&&&&L&=&W&+&8&& \\
    &&(L&+&2)(W&+&2)&=&L&\cdot &W&+&60 \\ \\
    (W&+&8&+&2)(W&+&2)&=&(W&+&8)W&+&60 \\
    &&W^2&+&12W&+&20&=&W^2&+&8W&+&60 \\
    &&-W^2&-&8W&-&20&&-W^2&-&8W&-&20 \\
    \midrule
    &&&&&&\dfrac{4W}{4}&=&\dfrac{40}{4}&&&& \\ \\
    &&&&&&W&=&10&&&& \\
    &&&&&&L&=&10&+&8&=&18
    \end{array}\)