Question

Henry is planning to create two rectangular gardens. Part A

Henry has 96 feet of fencing to enclose the first rectangular garden. The garden will be x feet wide.
Which function, f(x), can Henry use to determine the area, in square feet, of the first garden?
a f(x) = 48x
f(x) = 48 - x
f(x) = 48 – x²
f(x) = 48x - x2

Answer 1

f(x) = 48x - x^2

Explanation:

The 96 feet of fencing must be sufficient to cover the entire outer perimeter of the first rectangular garden.

Perimeter, P (feet) = 2*(width) + 2*(length)

width is x, length is l

P = x*l

We are given only the width. We also need the length. We can determine a length by subtracting 2 x from P (96 feet) to find 2l:

96ft - 2x = 2l

l = (96-2x)/2

l = 48 - x

The total area is thus (x*(48-x)), or 48x - x^2