need help with math problem

Question

Among all rectangles that have a perimeter of 110 , find the dimensions of the one whose area is largest.  Write your answers as fractions reduced to lowest terms.

Answer 1

First you want to divide the perimeter by 2

Then you should consider numbers that sum to half the perimeter but multiply to the largest area

P = 110 = 2L + 2W

Divide both sides of the equation by 2

55 = L + W

What numbers sum to 55 and multiply to the largest area

For example

20 + 35 = 55

20 x 35 = 700

21.5 + 33.5 = 55

21.5 x 33.5 = 720.25

Give it a try see if you can come up with larger areas than 756 that fit the criteria there are a few.