SOLUTION: The shaded rectangle is twice as long as it is wide. The perimeter of the rectangle is 30cm. What is the area of the rectangle?

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Question 976837: The shaded rectangle is twice as long as it is wide.
The perimeter of the rectangle is 30cm.
What is the area of the rectangle?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w and L, width and length

FORMULAS
wL=A for area
2w+2L=p for perimeter

DESCRIPTION
system%28L=2w%2Cp=30%29

Look at system:
system%28wL=A%2C2w%2B2L=p%2CL=2w%29

w%2A2w=A
2w%5E2=A
-
2w%2B2%2A2w=p
6w=p
highlight_green%28w=p%2F6%29
-
2L=p-2w
2L=p-2%28p%2F6%29
2L=p-p%2F3
2L=%283p-p%29%2F3
2L=2p%2F3
highlight_green%28L=p%2F3%29

p was given a value, 30, but L and w were only described as unknown variables. Now, they can be evaluated in terms of p.

Question was, find area.
A=wL
A=%28p%2F6%29%28p%2F3%29
highlight%28A=%28p%5E2%29%2F18%29


highlight%28highlight_green%28A=50%29%29