SOLUTION: the perimeter of a square is 40ft. find the length of a diagonal of the square to the nearest tenth

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Question 538105: the perimeter of a square is 40ft. find the length of a diagonal of the square to the nearest tenth
Answer by fcabanski(1391) About Me  (Show Source):
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For a square P=4s. That means each side s=p/4 = 40/4=10.


The diagonal of a square makes a right triangle with two sides. The diameter is the hypotenuse (h) of that right triangle.


Pythagorean Theory h%5E2=s%5E2%2Bs%5E2=2s%5E2 so h+=+sqrt%282s%5E2%29.
Plug s=10 into that formula.


h=sqrt%282%2810%5E2%29%29+=+sqrt%282%2A100%29+=10%2Asqrt%282%29=+14.1 ft.

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