SOLUTION: The hypotenuse of an isosceles right triangle is 3 cm longer than either of its legs. Find the exact length of each side

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Question 436003: The hypotenuse of an isosceles right triangle is 3 cm longer than either of its legs. Find the exact length of each side
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
If it's an isosceles right triangle, then the legs are equal, therefore:
x2+x2=(x+3)2
2x2=x2+6x+9
x2-6x-9=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B-9+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A1%2A-9=72.

Discriminant d=72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+72+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+72+%29%29%2F2%5C1+=+7.24264068711928
x%5B2%5D+=+%28-%28-6%29-sqrt%28+72+%29%29%2F2%5C1+=+-1.24264068711928

Quadratic expression 1x%5E2%2B-6x%2B-9 can be factored:
1x%5E2%2B-6x%2B-9+=+1%28x-7.24264068711928%29%2A%28x--1.24264068711928%29
Again, the answer is: 7.24264068711928, -1.24264068711928. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B-9+%29

Throwing out the negative answer, the legs are 7.24264 cm., the hypotenuse is 10.24264 cm..