SOLUTION: Which one is greater...The diagonal of a rectangle or half the perimeter of the same rectangle?

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Question 413058: Which one is greater...The diagonal of a rectangle or half the perimeter of the same rectangle?
Found 2 solutions by rfer, Theo:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
1/2 perimeter is greater

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Half the perimeter of the rectangle is greater.

The diagonal cuts the rectangle in half and makes 2 right triangles out of it.

in a right triangle, the sum of the 2 legs of the triangle is always greater than the hypotenuse.

the diagonal of the rectangle is the hypotenuse of the 2 right triangles formed by it.

consider a 3,4,5 right triangle (common one).

c^2 = a^2 + b^2 means 5^2 = 3^2 + 4^2 means 25 = 9 + 16 = 25.

3 + 4 is greater than 5 (sum of 2 legs is greater than the hypotenuse).