SOLUTION: The length of a rectangle is six times its width. If the area of the rectangle is 486 cm^2 , find its perimeter.

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Question 731877: The length of a rectangle is six times its width. If the area of the rectangle is 486 cm^2 , find its perimeter.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The length of a rectangle L is six times its width W:
L=6W......eq. 1

If the area A=L%2AW of the rectangle is 486cm%5E2 , find its perimeter P
start with
A=L%2AW...plug in given value for area
486cm%5E2=L%2AW...substitute L from eq. 1
486cm%5E2=6W%2AW......solve for W
486cm%5E2=6W%5E2
486cm%5E2%2F6=W%5E2
81cm%5E2=W%5E2
W=sqrt%2881cm%5E2%29
highlight%28W=9cm%29
now go back to eq. 1 and find L
L=6W......eq. 1
L=6%2A9cm
highlight%28L=54cm%29

now we can find perimeter P
P=2L%2B2W
P=2%2A54cm%2B2%2A9cm
P=108cm%2B18cm
highlight%28P=126cm%29