Question

A rancher wants to fence a rectangular pasture along a straight riverbank. He has 350 yards of fencing to enclose the other three sides of the pasture. If one side of the pasture has to be three times as long as the other, what is the area of the pasture? Find all possible answers. PLEASE LOOK AT THIS: The area can be ______ or _______ square yards. Thanks for answering!

Answer 1

• 7500 or 14700 square yards

Explanation:

Let the sides be x and y

3 sides sum to

• 2x + y = 350 or
• x + 2y = 350

If one side is 3 times the other then we have

• x = 3y

The sums above become:

• 2x + y = 350 ⇒ 2(3y) + y = 350 ⇒ 7y = 350 ⇒ y = 50 and x = 150
• x + 2y = 350 ⇒ 3y + 2y = 350 ⇒ 5y = 350 ⇒ y = 70 and x = 210

The area in each case is:

• 50*150 = 7500 square yards
• 70*210 = 14700 square yards