SOLUTION: the length of a rectangle is twice as long as its width. Express the area of the rectangle as a function of its perimeter

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Question 273321: the length of a rectangle is twice as long as its width. Express the area of the rectangle as a function of its perimeter
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The first thing we know is that

The next thing we know is that the perimeter of a rectangle is given by:



Substituting we discover that:



or



The area of a rectangle is given by:



Substituting:



Check the answer for reasonability:

Consider a 2' by 4' rectangle.

The area is 8 ft². The perimeter is 2 times 4 plus 2 times 2 equals 8 plus 4 equals 12'



Seems to work.


John