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Sagot :
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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