A rectangle has a length of 2x and its width is 4 cm less than its length. The area of the rectangle is 80 square centimeters.

Question

a) Write a simplified expression for the area of the rectangle (expand and simplify).

b) A square has an area that is 3x2 + 4 square cm less than the area of the rectangle.

    Write a simplified expression for the area of the rectangle (combine like terms).   

c) Determine binomial expressions for the length and width of the rectangle by factoring. 

Answer 1

L=2x

W=2x-4

A=LW = 2x(2x-4) = 4x^2 -8 = Area of the rectangle

with sides 2x and 2x-4

Area of Square = 4x^2 -8 - (3x^2 +4) = x^2 -12