SOLUTION: the hypotenuse of an isosceles right triangle is one meter longer than either of its legs. find the exact length of each side.

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Question 738771: the hypotenuse of an isosceles right triangle is one meter longer than either of its legs. find the exact length of each side.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If it's isosceles, then both legs are equal
Let +x+ = length of one of the legs
+x%5E2+%2B+x%5E2+=+%28+x+%2B+1+%29%5E2+
+2x%5E2+=+x%5E2+%2B+2x+%2B+1+
+x%5E2+-+2x+-+1+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-2+
+c+=+-1+
+x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2+-+4%2A1%2A%28-1%29+%29%29+%2F+%282%2A1%29+
+x+=+%28+2+%2B-+sqrt%28+4+%2B+4+%29%29+%2F+2+
+x+=+%28+2+%2B-+sqrt%28+8+%29%29+%2F+2+
+x+=+%28+2+%2B+2%2Asqrt%282%29+%29+%2F+2+
+x+=+1+%2B+sqrt%282%29+ answer
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check:
+2x%5E2+=+%28+x+%2B+1+%29%5E2+
+2%2A%28+1+%2B+sqrt%282%29+%29%5E2+=+%28+2+%2B+sqrt%282%29+%29%5E2+
+2%2A%28+1+%2B+2%2Asqrt%282%29+%2B+2+%29+=+4+%2B+4%2Asqrt%282%29+%2B+2+
+6+%2B+4%2Asqrt%282%29+=+6+%2B+4%2Asqrt%282%29+
OK