Question

A farmer needs to enclose three sides of a meadow with a fence (the fourth side is a river). The farmer has 30 feet of fence and wants the meadow to have an area of 112 sq-feet. What should the dimensions of the meadow be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.)

Answer 1

Width = 7 feets ; length = 16 feets

Explanation:

Given the following :

Area of meadow = 112 sq feet

Width = W (smaller dimension and 2 sides)

Length = L (longer dimension and 1 side)

Yards of fence = 30 feets ;

Hence,

L + W = 30

L + 2W = 30

L = 30 - 2W - - - (1)

Recall:

Area = L * W = 112

Substitute value of L

112 = (30 - 2W) * W

112 = 30W - 2W²

2W² - 30W + 112 = 0

W² - 15W + 56 = 0

W² - 8W - 7W + 56 = 0

W(W - 8) - 7(W - 8) = 0

(W - 8) = 0 or (W - 7) =0

W = 8 or W = 7

Since length should be as long as possible, we take the shorter width :

W = 7

L + 2W = 30

L = 30 - 14

L = 16 feets