SOLUTION: The diagonal of a square is 2 cm. longer than its side. Find its side.

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Question 210961: The diagonal of a square is 2 cm. longer than its side. Find its side.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem:c%5E2+=+a%5E2%2Bb%5E2
In the square, let the sides be s and the diagonal be d.
d%5E2+=+s%5E2%2Bs%5E2 But d = s+2, so substitute:
%28s%2B2%29%5E2+=+s%5E2%2Bs%5E2 Simplify.
s%5E2%2B4s%2B4+=+2s%5E2 Subtract s%5E2 from both sides.
4s%2B4+=+s%5E2 Subtract (4s+4) from both sides.
s%5E2-4s-4+=+0 Use the quadratic formula to solve for s.
s+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a and in this equation, a = 1, b = -4, and c = -4. Make the appropriate substitutions:
s+=+%28-%28-4%29%2B-sqrt%28%28-4%29%5E2-4%281%29%28-4%29%29%29%2F2%281%29 Evaluate:
s+=+%284%2B-sqrt%2816-%28-16%29%29%29%2F2
s+=+2%2B2sqrt%282%29 or s+=+2-2sqrt%282%29
s+=+4.83 or s+=+-0.83 Discard the negative solution as lengths are positive values.
highlight%28s+=+4.83%29cm.