A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.

1] Find a function that models the total area of the four pens. (Let w be the width of the rectangular area and A (w) be the area.)

2]Find the largest possible total area of the four pens. (Round your answer to one decimal place.)

Question

Mathematics

Killian Burch

11 April, 11:36

A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.

1] Find a function that models the total area of the four pens. (Let w be the width of the rectangular area and A (w) be the area.)

2]Find the largest possible total area of the four pens. (Round your answer to one decimal place.)

+3

Answers (1)

Know the Answer?

Joseph Tyler · Answer 1

2 W + 5 L = 750 ft

5 L = 750 - 2 W

L = 150 - 2 W / 5

A (W) = W * (150 - 2 W / 5)

A function that models the total area:

A (W) = 150 W - 2 W² / 5

A' (W) = 150 - 4 W / 5

150 - 4 W / 5 = 0

4 W / 5 = 150

W = 187.5 ft

The largest possible area:

A = 150 * 187.5 - (2 * 187.5²) / 5 = 28,125 - 14,062.5 = 14,062.5 ft²