Chapter 9.5, Problem 9CYU

To determine

Find the solution.

Answer to Problem 9CYU

Length = 18 ft.

Width = 8 ft.

Explanation of Solution

Given Information: Area of Deck = $144f{t}^2$ , Width = w, Length l = $w+10$

Formula Used : Area of Deck = $Lenght\times Width$ , $a^2+2ab+b^2={(a+b)}^2$ and

  $a^2-b^2=(a+b)(a-b)$

Calculation:

Area of Deck = $144f{t}^2$ , Width = w, Length l = $w+10$

Area of Deck = $Lenght\times Width$

  $144=\left(w+10\right)\times w$

So,

  $144=w^2+10w$

Now, simplify

  $w^2+10w-144=0$

Now, adding & subtracting the square of half the coefficient of w.

  $w^2+10w-144+{\left(\frac{10}{2}\right)}^2-{\left(\frac{10}{2}\right)}^2=0$

Now use formula, $a^2+2ab+b^2={(a+b)}^2$

  ${\left(w+5\right)}^2-144-5^2=0$

So,

  ${\left(w+5\right)}^2-144-25=0$

So,

  ${\left(w+5\right)}^2-169=0$

Now, square root of 169 is 13

  ${\left(w+5\right)}^2-{\left(13\right)}^2=0$

Now use formula, $a^2-b^2=(a+b)(a-b)$

  $\left(w+5+13\right)\left(w+5-13\right)=0$

Now,

  $\left(w+18\right)\left(w-8\right)=0$

Hence,

  $w=-18$ or $w=8$

Width w = 8 ft.

Length l = $w+10=8+10=18$ ft.