Question

1. A farmer wants to build a fence around a rectangular area of his farm with one side of the region against his barn. He has 76 feet of fencing to

use for the three remaining sides. What dimensions will make the largest area for the region?

Answer 1

19 ft by 38 feets

Explanation:

Given that :

Available fencing = 76 feets

Rectangular fencing with 3 sides

Let the 3 sides be :

x, x, y

x + x + y = 2x + y = 76

y = 76 - 2x

Area = x * y = xy

Area = (76 - 2x) * x

Area = 76x - 2x²

Take derivative of Area with respect to x ; dA

dA /dx = 76 - 4x = 0

76 - 4x = 0

-4x = - 76

x = 76 / 4

x = 19

2x + y = 76

2(19) + y = 76

38 + y = 76

y = 76 - 38

y = 38

Hence, dimension : 19feet by 38 feets