SOLUTION: luke road his bike on a trail that formed a right triangle. One leg of the right triangle was 5 kilometers longer than the other leg. they hypotenuse of the right triangle was 25

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Question 269818: luke road his bike on a trail that formed a right triangle. One leg of the right triangle was 5 kilometers longer than the other leg. they hypotenuse of the right triangle was 25 kilometers long. How far did he ride all together?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The three sides are: x, x+5, 25. By Pythagorean theorem we get
(i) x%5E2+%2B+%28x%2B5%29%5E2+=+25%5E2
expanding, we get
(ii) x%5E2+%2B+x%5E2+%2B+10x+%2B+25+=+625
combine like terms to get
(iii) 2x%5E2+%2B+10x+%2B+25+=+625
set = 0 to get
(iv) 2x%5E2+%2B+10x+-+600+=+0
factor to get
(v) %282x-30%29%28x%2B20+%29+=+0
So,
x = 15
or
x = -20
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The three sides are: 15, 20, and 25