Chapter 9.4, Problem 9CYU

To determine

To calculate: The expression total time for the trip.

Answer to Problem 9CYU

The required dimension is $18\times 8\text{square}\text{feet}$ .

Explanation of Solution

Given information:

The area od the deck is 144 square feet.

Length is 10 feet more than the width.

Formula Used:

Area of a rectangle is $\text{Area}=\text{Lnegth}\times \text{Width}$ .

Roots of a quadratic equation is $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

Let $w$ be the width of the deck.

Given that length is 10 feet more than its width.

Thus, length is $10+w$ .

Now, find the area, use the area formula for a rectangle.

  $\text{Area}=\text{Lnegth}\times \text{Width}$

Substitute the values, $10+w$ for length and $w$ for width.

  $144=\left(10+w\right)\times w$

Now, solve the above equation for $w$ .

  $\begin{array}{l}144=10w+w^2\\ 144=w^2+10w\end{array}$

Rewrite the above equation.

  $w^2+10w-144=0$

Now, use the formula $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ to find $w$ .

  $\begin{array}{c}w=\frac{-10\pm \sqrt{{10}^2-4\times 1\times \left(-144\right)}}{2\times 1}\\ =8\text{feet}\end{array}$ [here the negative part is discarded since length cannot be negative]

Now, find length.

  $\begin{array}{c}\text{Length}=10+8\\ =18\text{feet}\end{array}$

Hence the required dimension is $18\times 8\text{square}\text{feet}$ .