Question below:

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 meters of fence and wants the meadow to have an area of 128 sq-meters. 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.)

length = _____ meters

width = _____ meters

Enter your answers as numbers. If necessary, round to the nearest hundredths.

Answer 1

Let x be the width and y be the length.

2x+y = 32 m

xy =128 m²

y = 128/x

2x+128/x = 32

2x²-32x +128 = 0

x²-16x+64=0

(x-8)(x-8) = 0

x=8 meters = Width

y = 128/8 = 16 meters = Length