Find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing. (Assume that the length is greater than or equal to the width.) ft length width ft Tutorial Additional Materials eBook Example Video

Answer:Dimensions are of one corral is:

Length=50ft

Width = 37.5ft

Combined area=1875ft

Step-by-step explanation:

Let L = length

Let w = width

There are 3 pieces of fencing: 3L + 4w = 300

W = (300 - 3L) / 4 ... equation 1

Combined area of the corrals is given by:

A = L * 2w ... eq2

Put eq1 into eq2

A = L * 2 (300-3L) / 4

A = 1/2 (300 - 3 L) ^2

A = - (3/2) L^2 + 150

Using - b/2a to solve for L in the quadratic equation

-150/2 (3/2) = (150*2) / (2*3)

L = 50ft

W = 300-3 (50) / 4

W=150/4=37.5ft

Combined are=50*37.5=1875ft