Question

The area of a rectangle trampoline is $112f{t}^2.$

The length of the trampoline is $6ft$ greater than the width of the trampoline, this situation can be represented by the equation $w^2+6w-112=0$

What is the length of the trampoline in feet?

• A. $7$
• B. $16$
• C. $8$
• D. $14$

Answer 1

The correct option is D

$14$

Explanation for the correct option :

Option (C):

Find the area of the rectangle trampoline:

Let the width be $w.$

As the length is $6$ feet greater than the width,

so the length will be $w+6$.

Area of the trampoline is calculated as:

$$\begin{gathered} Area=\mathrm{length}\times \mathrm{width} \\ =(w+6)\times w \\ =w^2+6w \end{gathered}$$

Solve the equation:

As given, $w^2+6w-112=0$

Therefore, the area is$112$, so

$$\begin{gathered} w^2+6w=112 \\ {w}^2+6w-112=0 \end{gathered}$$

Factoring,

$\begin{array}{rcl}{w}^2-8w+14w-112& =& 0\\ w(w-8)+14(w-8)& =& 0\\ (w-8)(w+14)& =& 0\end{array}$

So, $w=8$ and $w=-14$ (Width can't be negative)

Therefore, $\mathrm{width}=8\mathrm{feet}$

The length of the trampoline is,

$$\begin{gathered} w+6=8+6 \\ =14\mathrm{feet} \end{gathered}$$

Hence, option $\left(D\right)$ is the correct answer.

The explanation for incorrect options:

The obtained value is $14feet$ which is not equivalent to option $\left(A\right)$,option $\left(B\right)$ and option $\left(C\right)$.

Hence, option (A), option (B), option (C), are all incorrect.