Fence for Garden using polynomial???

Question

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

Answer 1

Here's what we know:

P_rec = 2l + 2w

A_rec = lw

l = 2w - 5

 

Since we have a value for l, we can use that for our equation:

A)

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

P = 4w - 10 + 2w

P = 6w - 10

 

B)

A = (2w - 5)w

A = 2w² - 5w

 

C)

P = 6 * 8 - 10

P = 48 - 10

P = 38 feet

 

A = 2 * 8² - 5 * 8

A = 2 * 64 - 40

A = 128 - 40

A = 88 ft²

 

Answer 2

 

Rein,

 

length is five less than two times the width => length = 2width -5

(A) perimeter = length + width = 2(2width - 5 + width) + 2width

(B) area = length * width = (2width - 5)((width)

(C) perimeter = 2width + 2length = 2(2width - 5 + width) + 2width = 2(2(8) -5 + 8) = ?

(D) area = (2width - 5)((width) = (2(8)-5)(8) = ?

I hope this helps Rein