A rectangle with a perimeter of 30 centimeters is twice as long as it is wide. What is the area of the rectangle in square centimeters  

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lfryerda | High School Teacher | (Level 2) Educator

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If the width of the rectangle is x and the length of the rectangle is y, then the perimeter of the rectangle is `2(x+y)=30` and the area of the rectangle is `A=xy` .  Also, we are told that the length is twice the width, so `y=2x` .  This can be substituted into the perimeter equation:

`2(x+y)=30`  divide by 2

`x+y=15`  sub in `y=2x`

`x+2x=15`  simplify left side

`3x=15`  divide by 3

`x=5`  which means `y=2(5)=10`

Then the area of the rectangle is `A=5(10)=50` square centimeters.

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