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).

Question

A farmer needs to enclose three sides of a meadow with a fence (the fourth side is a cliff wall). The farmer has 32 feet of fence and wants the meadow to have an area of 128 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.)

what is the length

what is the width

Answer 1

Let W be the width and L the length.

Two relations hold

a. 2W + L = 32

b. W x L = 128

Solve a. for L to get L = 32 - 2W

Substitute this L in b.

W x (32 - 2W) = 128

Solve for W: -2W² +32W -128 = 0. This can be rewritten as W² - 16W + 64 = 0

Using the quadratic formula, you get W = 8 , then L= 16