Question

Two equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting a fence across its middle. If each lot is to contain 2,700 square feet, what is the minimum amount of fence (in ft) needed to enclose the lots (include the fence across the middle)

Answer 1

360 feet

Explanation:

Area = 2XY = 2 · 2,700 = 5,400

Perimeter = (2 · 2X) + 3Y = 4X + 3Y

Y = 5,400 / 2X = 2,700 / X

Perimeter = 4X + 8,100/X

P'(x) = 4 - 8,100/X² = 0

4 = 8,100/X²

X² = 8,100 / 4 = 2,025

X = √2,025 = 45

Y = 2,700 / 45 = 60

Perimeter = (4 · 45) + (3 · 60) = 180 + 180 = 360 feet