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 w^2 + 6w - 112 = 0.
what is the width of the trampoline in feet?
a 7ft
b 16ft
c 8ft
d 14ft

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:

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

where \( a = 1 \), \( b = 6 \), and \( c = -112 \).

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

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

Now we can find \( w \):

\[
w = \frac{{-6 \pm \sqrt{484}}}{2(1)}.
\]

The square root of 484 is 22:

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

This gives us two possible solutions:

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

2.
\[
w = \frac{{-6 - 22}}{2} = \frac{-28}{2} = -14.
\]

Since the width cannot be negative, we ignore the second solution. Thus, the width of the trampoline is:

\[
w = 8 \text{ ft}.
\]

Therefore, the answer is **c) 8 ft**.