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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 :

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Answer:Answer: (a) = P = 2(x + 2x-5) = 2(3x-5) = 6x - 10.

Step-by-step explanation:

Part a : Polynomial represents the perimeter of the garden is 6W-10

Part b : Polynomial represents the area of the garden is [tex]2w^{2}-5w[/tex]

Part c : Perimeter = 38 feet and area = 88 feet square

What is polynomial?

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables

What is perimeter?

A perimeter is a closed path that encompasses, surrounds

What is area?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface

Given,

Length is five less than two times the width

Consider

L is the length and W is the width

Then,

L=2W-5

Part a

Perimeter = 2(L+W)

Substitute the value of L

P=2(L+W)

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

P=2(2W-5+W)

P=2(3W-5)

Perimeter= 6W-10

Part b

Area of the garden = L×W

Area = (2W-5)W

Area = [tex]2w^{2}-5w[/tex]

Part c

Given width W = 8 feet

Perimeter = 6W-10

P=6×8-10

Perimeter =38 feet

Area = [tex]2w^{2}-5w[/tex]

Area=[tex]2(8^{2})-5(8)[/tex]

Area = 88 feet square

Hence,

Part a : Polynomial represents the perimeter of the garden is 6W-10

Part b : Polynomial represents the area of the garden is [tex]2w^{2}-5w[/tex]

Part c : Perimeter = 38 feet and area = 88 feet square

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