Question

#14.
The area of a rectangular trampoline is 112 ft
2. The length of the trampoline is 6 ft greater than the width of the trampoline. This situation can be represented by the equation
w2+6w−112=0.



What is the width of the trampoline in feet?

Answer 1

To solve for the width \( w \) of the trampoline using the equation \( w^2 + 6w - 112 = 0 \), we can either factor the quadratic equation or use the quadratic formula. In this case, let's try to factor it.

We need to find two numbers that multiply to \(-112\) (the constant term) and add to \(6\) (the coefficient of \(w\)).

The factors of \(-112\) that satisfy this are \(14\) and \(-8\), since:
\[
14 \times (-8) = -112 \quad \text{and} \quad 14 + (-8) = 6.
\]

Thus, we can factor the quadratic as:
\[
(w + 14)(w - 8) = 0.
\]

Setting each factor equal to zero gives us:
\[
w + 14 = 0 \quad \Rightarrow \quad w = -14 \quad \text{(not a valid width)},
\]
\[
w - 8 = 0 \quad \Rightarrow \quad w = 8.
\]

The only valid solution for the width of the trampoline is:
\[
\boxed{8} \text{ feet}.
\]