Question

You need to construct fence around an area of 3136 ft2. What are the dimensions of the rectangular pen that minimize the amount of material needed

Answer 1

Answer:

Step-by-step explanation:

The the area of the rectangular pen be A = LW

L is the length

W is the width

Given

A = 3136ft²

3136 = LW..........1

Given the perimeter P = 2L+2W....... 2

From 1; L = 3136/W

Substitute into 2

P = 2(3136/W)+2W

P = 6272/W + 2W

In order to minimize the amount of material needed, then dP/dW = 0

dP/dW = -6272/W² + 2

0 = -6272/W² + 2

6272/W² = 2

cross multiply

6272 = 2W²

W² = 3136

W = √3136

W = 56ft

Since A = LW

3136 = 56L

L = 3136/56

L = 56ft

Hence the dimensions of the rectangular pen that minimize the amount of material needed is 56ft by 56ft