SOLUTION: This is my math question but im not sure how to solve it. One leg of a right triangle is 6in. longer than the other leg, the hypotenuse of the triangle is 25in. What is the length

Algebra ->  Triangles -> SOLUTION: This is my math question but im not sure how to solve it. One leg of a right triangle is 6in. longer than the other leg, the hypotenuse of the triangle is 25in. What is the length       Log On


   

Question 553647: This is my math question but im not sure how to solve it. One leg of a right triangle is 6in. longer than the other leg, the hypotenuse of the triangle is 25in. What is the length of each leg to the nearest inch? Please help :)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the length (in inches) of the shorter leg.
Then, the length (in inches) of the other leg would be
x%2B6
Pythagoras' theorem, applied to that triangle, tells you that
%28x%2B6%29%5E2%2Bx%5E2=25%5E2 --> x%5E2%2B12x%2B36%2Bx%5E2=25%5E2
--> 2x%5E2%2B12x%2B36-25%5E2=0 --> 2x%5E2%2B12x-589=0
Using the quadratic formula we find 2 values for x
,
but we can only use the positive solution
x+=%28-12+%2B-+sqrt%284856%29%29%2F4=-3+%2B-+sqrt+%281214%29%2F2 = approximately 14.42125 .
Then, the other leg length is about 6%2B14.42125=20.42125 .
So the leg lengths, to the nearest inch, are 14 inches and 20 inches.