SOLUTION: a diagonal of a square is 6 inches long. find its permiter and its area.

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Question 585516: a diagonal of a square is 6 inches long. find its permiter and its area.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Apply the Pythagorean theorem:
The diagonal (6 inches) of the square is the hypotenuse of a right triangle whose legs are s and s.
6%5E2+=+s%5E2%2Bs%5E2 Simplify.
36+=+2s%5E2 Divide by 2.
18+=+s%5E2 Take the square root.
s+=+sqrt%2818%29 Simplify.
s+=+3sqrt%282%29
Perimeter (P):
P+=+4s
P+=+4%2A3sqrt%282%29
P+=+12sqrt%282%29inches. and...
Area A+=+s%5E2
A+=+18sq.in.