Among all rectangles that have a perimeter of 134, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.

The answer to this question would be: L = 33.5, W=33.5

In this question, the rectangle has a perimeter of 134. From this number, you can get this equation:

perimeter=134

2 (L+W) = 134

L+W=67

L = 67-W

Using the formula for dimension you can get this equation:

dimension = L * W

dimension = (67-W) W = 67W - W^2

The maximum dimension should be differentiation of the equation which will look like:

67 - 2w = 0

2w = 67

w = 33.5