Question

Joe is commissioned to build a small rectangular garden area on community property. The landscape committee requested that the garden be 10 feet longer than it is wide. Joe has up to 90 feet of material to use for the perimeter. What is the maximum width w of the garden?

Write an expression that represents the length of the garden.

Write the inequality that models the perimeter of the garden.

Solve the inequality.

Answer 1

length = width + 10

4*width + 20 ≤ 90

width ≤ 17.5 feet

Explanation:

The perimeter of a rectangle is given by:

Perimeter = 2*length + 2*width

The length needs to be 10 feet longer than the width, so we have:

length = width + 10

Using this length in the perimeter equation, we have:

Perimeter = 2*(width + 10) + 2*width = 4*width + 20

The perimeter needs to be up to 90 feet, so we have:

P ≤ 90

4*width + 20 ≤ 90

4*width ≤ 70

width ≤ 17.5 feet

the maximum width of the garden is 17.5 feet