Among all rectangles that have a perimeter of 210, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

Let the length of the rectangle be x units then the width = (210 - 2x) / 2

= 105 - x units

Area A = x (105 - x) = 105x - x^2

Finding the derivative:_

dA/dx = 105 - 2x = 0 for max/minm volume

x = 52.5

this is for a maximum area because second derivative is negative ( = - 2).

width = 105 - 52.5 = 52.5

Dimension for maximum area = 52 1/2 * 52 1/2. (The rectangle is actually a square).