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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?

Sagot :

MrRoyal

Answer:

[tex]Perimeter = 12y[/tex]

Step-by-step explanation:

Given

[tex]Area = 18y^2 - 8[/tex] -- two rectangles

Required

Determine the perimeter of one of the rectangles

First, calculate the area (A) of 1 rectangle

[tex]A =\frac{1}{2}Area[/tex]

[tex]A =\frac{1}{2}(18y^2 - 8)[/tex]

[tex]A =9y^2 - 4[/tex]

Express as difference of two squares

[tex]A =(3y - 2)(3y+2)[/tex]

Area is calculated as:

[tex]A = Length * Width[/tex]

So, by comparison:

[tex]Length = 3y - 2[/tex]

[tex]Width = 3y + 2[/tex]

The perimeter is:

[tex]Perimeter = 2 *(Length + Width)[/tex]

[tex]Perimeter = 2 *(3y-2+3y+2)[/tex]

Collect Like Terms

[tex]Perimeter = 2 *(3y+3y-2+2)[/tex]

[tex]Perimeter = 2 *(6y)[/tex]

[tex]Perimeter = 12y[/tex]

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