SOLUTION: One leg of a right triangle is 3 cm longer than the other leg. The length of the hyptenuse is 10 cm. Find the length of each side.

Algebra ->  Pythagorean-theorem -> SOLUTION: One leg of a right triangle is 3 cm longer than the other leg. The length of the hyptenuse is 10 cm. Find the length of each side.       Log On


   

Question 368728: One leg of a right triangle is 3 cm longer than the other leg. The length of the hyptenuse is 10 cm. Find the length of each side.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%28x%2B3%29%5E2=10%5E2
x%5E2%2Bx%5E2%2B6x%2B9=100
2x%5E2%2B6x-91=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A2%2A%28-91%29+%29%29%2F%282%2A2%29+
x+=+%28-6+%2B-+sqrt%28+36%2B728+%29%29%2F%284%29+
x+=+%28-6+%2B-+sqrt%28+764+%29%29%2F%284%29+
x+=+%28-6+%2B-+2%2Asqrt%28+191+%29%29%2F%284%29+
x+=+%28-3+%2B-+sqrt%28+191+%29%29%2F%282%29+
Only the positive result makes sense for this problem.
highlight%28x+=+%28-3+%2B+sqrt%28+191+%29%29%2F%282%29%29+
or approximately,
x=5.41
.
.
x%2B3+=+%28-3+%2B+sqrt%28+191+%29%29%2F%282%29%2B6%2F2+
highlight%28x%2B3+=+%283+%2B+sqrt%28+191+%29%29%2F%282%29%29+
or approximately,
x=8.41