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

Answer:

$Perimeter = 12y$

Step-by-step 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

$A =\frac{1}{2}Area$

$A =\frac{1}{2}(18y^2 - 8)$

$A =9y^2 - 4$

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

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

$Perimeter = 2 *(6y)$

$Perimeter = 12y$