Polynomial Word Problem

Question

You are making a fence for your garden. The length is five less than two times the width. Write a polynomial that represents the perimeter of the garden. Write a polynomial that represents the area of the garden. Find the perimeter and area of the garden when the width is 8 feet.

Answer 1

Hi Faris,

 

You want to think about what you are being asked to describe. The garden is fenced by a rectangle. Therefore;

Area = length * width

and

Perimeter = 2*length + 2*width

 

The harder translation into math comes with the sentence: "The length is five less than two times the width." That translates to:

Length = 2*width - 5

because the "five less than" is another way of saying "minus 5"

 

Substituting the length equation into the other equations, we get:

a = (2w - 5)w

a = 2w² - 5w

a = 2(8)² - 5(8)

a = 128 - 40

a = 68 square feet

 

p = 2(2w - 5) + 2w

p = 4w - 10 + 2w

p = 6w - 10

p = 6(8) - 10

p = 48 - 10

p = 38 feet