SOLUTION: A parallelogram has two congruent diagonals of length 13. If one side has length 5, what is the perimeter of the parallelogram?

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Question 403206: A parallelogram has two congruent diagonals of length 13. If one side has length 5, what is the perimeter of the parallelogram?
Answer by solver91311(24713) (Show Source):
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Since the diagonals are congruent, the parallelogram must be a rectangle. That means either of the diagonals is the hypotenuse of a right triangle with adjacent sides of the rectangle as legs. Recognize that 5-12-13 is a Pythagorean Triple, hence the remaining leg must measure 12. Or use the Pythagorean Theorem and solve:

for giving you the other dimension of the rectangle.

Finally, use the formula for the perimeter of a rectangle to calculate the perimeter:

John

My calculator said it, I believe it, that settles it