Question

You are a landscaper, and you are designing a fence to enclose part of a yard. The section to be enclosed is rectangular and has a width of 21 feet and a length of 38 feet. What length of fence, in feet, will you need to enclose this part of the yard? 59 60 118 120 798

Answer 1

798

Explanation:

21x38=798

Answer 2

If you draw this out, you can see that total fence equation will be:

2L + 4W = 1200

Simplify, divide by 2

L + 2W = 600

L = (600-2W)

:

Area;

A = L*W

Substitute (600-2W) for L:

A = (600-2W)*W

A = -2W^2 + 600W; a quadratic equation

:

The dimension that will produce the greatest area will be the "axis of symmetry

which is: x = %28-b%29%2F%282a%29

:

In this equation a=-2, b=600

W = %28-600%29%2F%282%2A-2%29

W = %28-600%29%2F%28-4%29

W = +150 ft is the width

:

Find the length

L = 600 - 2(150)

L = 300 ft is the length

:

We can say the a field 300 by 150 gives he greatest area

:

This illustrated on a graph where y axis is the area and x axis is the width:

Explanation: