Question

a rectangular pen with a perimeter of 60 ft is needed to house 3 pigs. determine the maximum area of the pen and the dimensions that yield the maximum area. please help! i have this second last unit to cover then i can finally graduate and apply for college i need your help!

Answer 1

225 ft.
15x15ft

Answer 2

Let L be the length and W be the width of the rectangular pen.

Perimeter = 2L + 2W = 60 or
L + W = 30 ---- (1)
Area A = L * W = L * (30 - L) = 30L - L^2

Complete the square: A = -(L^2 - 30L) = -{ (L - 15)^2 - 225 }

If A is plotted against L you will see an inverted parabola with vertex at (15, 225).

So the maximum area = 225 ft^2; L = 15 ft. and W = 15 ft.