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
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.