Length times width math problem

Question

Write and solve the inequality for the scenario below. Show all work for credit.

the length of a rectangle is 3 centimeters longer than the width. The perimeter of the rectangle is less than 15 centimeters

Answer 1

l > w + 3 --- first inequality

2 * (l + w) < 15 --- second inequality

Then, change the first inequality into the following by adding w, and multiply by 2

2 * (l + w) > 2 * (2w + 3)

So, now that,

2 * (2w + 3) < 2 * (l + w) < 15

2 * (2w + 3) < 15

2w + 3 < 7.5

2w < 4.5

w < 2.25

Usually question would ask for finding the maximum perimeter if l and w are whole number, in this case,

w = 2 and l = 5, so the maximum perimeter would be 14