Question

Among all the rectangles whose perimeters are 100 feet, find the dimensions of the one with the maximum area. explain step by step.

Answer 1

We let x be the length and y be the width of the rectangle. Then,

Perimeter = 2x + 2y
100 = 2x + 2y
50 = x + y
y = 50 - x

Area = xy
A = x(50 - x)
A = 50x - x^2

We then take the derivative; set it equal to zero:

A ' = 50 - 2x
0 = 50 - 2x
2x = 50
x = 25
y = 50 - x
y = 50 - 25
y = 25

Therefore, the dimensions are 25 and 25.