Question

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?



7 ft

16 ft

8 ft

14 ft

Answer 1

To find the width of the trampoline, we can solve the quadratic equation given:

\[ w^2 + 6w - 112 = 0. \]

We can use the quadratic formula, which is:

\[
w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this equation, \(a = 1\), \(b = 6\), and \(c = -112\).

First, we calculate the discriminant (\(b^2 - 4ac\)):

\[
b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot (-112) = 36 + 448 = 484.
\]

Next, we take the square root of the discriminant:

\[
\sqrt{484} = 22.
\]

Now we can substitute back into the quadratic formula:

\[
w = \frac{-6 \pm 22}{2 \cdot 1} = \frac{-6 \pm 22}{2}.
\]

This results in two possible solutions:

1.
\[
w = \frac{-6 + 22}{2} = \frac{16}{2} = 8,
\]

2.
\[
w = \frac{-6 - 22}{2} = \frac{-28}{2} = -14 \quad (\text{not valid, since width can't be negative}).
\]

So the width of the trampoline is:

\[
\boxed{8 \text{ ft}}.
\]