Among all rectangles that have a perimeter

Question

Among all rectangles that have a perimeter of 172, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

Answer 1

Rectangle's Perimeter:

2 length + 2 width =172

=> length + width = 86

Before we continue, it's important to know that to achieve the largest area, the rectangle's sides (length and width) should be as close as possible. A square has the largest area (a square is *technically* a rectangle!)

So, we assume length = width.

2 length = 86

length = 43

width = 43

43 * 43 = 1849 (largest area possible)