Question

The combined area of a pair of congruent rectangles can be represented, in square units, by the expression 18y^2-818y 2 −8. The length and side of each rectangle can be represented as a difference of squares. What is the perimeter of one of the rectangles?

Answer 1

`Perimeter = 12y`

Explanation:

Given

`Area = 18y^2 - 8` -- two rectangles

Required

Determine the perimeter of one of the rectangles

First, calculate the area (A) of 1 rectangle

`A =(1)/(2)Area`

`A =(1)/(2)(18y^2 - 8)`

`A =9y^2 - 4`

Express as difference of two squares

`A =(3y - 2)(3y+2)`

Area is calculated as:

`A = Length * Width`

So, by comparison:

`Length = 3y - 2`

`Width = 3y + 2`

The perimeter is:

`Perimeter = 2 *(Length + Width)`

`Perimeter = 2 *(3y-2+3y+2)`

Collect Like Terms

`Perimeter = 2 *(3y+3y-2+2)`

`Perimeter = 2 *(6y)`

`Perimeter = 12y`