SOLUTION: One side of the rectangle is 1 dm less than it's diagonal. If the perimeter of the rectangle is 62 dm, find the area of the rectangle.
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Question 636224: One side of the rectangle is 1 dm less than it's diagonal. If the perimeter of the rectangle is 62 dm, find the area of the rectangle.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
be the "one side" of the rectangle. Then 
is the diagonal.
With a tip 'o the hat to Mr. Pythagoras, we can say that the other side of the rectangle is:
^2\ -\ x^2})
So the missing side of the rectangle is 
The perimeter of a rectangle is 2 times the length plus 2 times the width so:
Solve the quadratic (it factors). One of the roots will be extraneous and you can tell by checking them in the original perimeter equation. Discard the extraneous root. Then calculate . Multiply the length times the width to get the area.
John
My calculator said it, I believe it, that settles it
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