You are making a fence for your garden. The length is five less that 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.
width --- w
length --- 2w - 5
Perimeter = 2 x width + 2 x length
= ...
area = (width)(length)
= ...
when w = 8
l = 16-5 = 11
take over
A. To write a polynomial that represents the perimeter of the garden, we need to find the sum of all the sides of the fence. Let's say the width of the garden is "w" feet.
The length of the garden is given as "five less than two times the width", which can be written as 2w - 5.
The perimeter of a rectangle is given by the formula: P = 2(length + width).
In this case, the perimeter can be represented by the polynomial:
P = 2(2w - 5 + w) = 2(3w - 5) = 6w - 10.
So, the polynomial that represents the perimeter of the garden is 6w - 10.
B. To write a polynomial that represents the area of the garden, we multiply the length and width of the rectangle. The width is given as "w" feet, and the length is 2w - 5 feet.
The area of the garden can be represented by the polynomial:
A = width × length = w × (2w - 5) = 2w^2 - 5w.
So, the polynomial that represents the area of the garden is 2w^2 - 5w.
C. To find the perimeter and area of the garden when the width is 8 feet, substitute the value of 8 for "w" in the previous expressions.
Perimeter: P = 6w - 10
Substituting w = 8: P = 6(8) - 10 = 48 - 10 = 38 feet
Area: A = 2w^2 - 5w
Substituting w = 8: A = 2(8^2) - 5(8) = 2(64) - 40 = 128 - 40 = 88 square feet
So, when the width is 8 feet, the perimeter of the garden is 38 feet, and the area is 88 square feet.