SOLUTION: if the perimeter of a rectangle is 20 feet anf the diagonal is 2 square root 13 feet, then what are the length and width?

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Question 173453: if the perimeter of a rectangle is 20 feet anf the diagonal is 2 square root 13 feet, then what are the length and width?
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
The perimeter of a rectangle is given by , so we know that .

Solving for :







The measure of a diagonal of a rectangle in terms of the length and width is given by the Pythagorean Theorem:

where is the measure of the diagonal.

But we know that:

Square both sides:



Now substitute the expression for in terms of developed earlier:



Expand, collect terms, and put into standard form for a quadratic:





Divide through by



Leaving you with a factorable quadratic to solve. Hint: and

Since you are solving for the width, pick the smaller of the two roots as your width and calculate the length from (which you will find is the other root of your quadratic)
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