Question

Two parts Someone please help!!!!!

Part one: Write a function rule for the area of a rectangle with a length of 2 ft less than three times its width.
Part two: what is the area of the rectangle when its width is 2 ft?

Answer 1

Part one: The function rule for the area of the rectangle is A(x) = 3x² - 2x

Part two: The area of the rectangle is 8 feet² when its width is 2 feet

Explanation:

Assume that the width of the rectangle is x

∵ The width of the rectangle = x feet

∵ The length of the rectangle is 2 ft less than three times its width

→ That means multiply the width by 3, then subtract 2 from the product

∴ The length of the rectangle = 3(x) - 2

∴ The length of the rectangle = (3x - 2) feet

∵ The area of the rectangle = length × width

∴ A(x) = (3x - 2) × x

→ Multiply each term in the bracket by x

∵ A(x) = x(3x) - x(2)

∴ A(x) = 3x² - 2x

∴ The function rule for the area of the rectangle is A(x) = 3x² - 2x

∵ The rectangle has a width of 2 ft

∵ The width = x

∴ x = 2

→ Substitute x by 2 in A(x)

∵ A(2) = 3(2)² - 2(2)

∴ A(2) = 3(4) - 4

∴ A(2) = 12 - 4

∴ A(2) = 8

∴ The area of the rectangle is 8 feet² when its width is 2 feet