SOLUTION: The shortest leg of a triangle is 7 inches shorter than the other leg. The hypotenuse of this triangle is 13 inches. What are the lengths of the two legs of this triangle?

Algebra ->  Rectangles -> SOLUTION: The shortest leg of a triangle is 7 inches shorter than the other leg. The hypotenuse of this triangle is 13 inches. What are the lengths of the two legs of this triangle?       Log On


   

Question 468907: The shortest leg of a triangle is 7 inches shorter than the other leg. The hypotenuse of this triangle is 13 inches. What are the lengths of the two legs of this triangle?
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
Let x - the shortest leg of a triangle
The shortest leg of a triangle is 7 inches shorter than the other leg, then the other leg is x%2B7 inches. The hypotenuse of this triangle is 13 inches.
Use the Pythagorean theorem x%5E2%2B%28x%2B7%29%5E2=13%5E2
x%5E2%2Bx%5E2%2B14x%2B49=169
2x%5E2%2B14x-120=0 Divide by 2
x%5E2%2B7x-60=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A1%2A%28-60%29+%29%29%2F%282%2A1%29+
x+=+%28-7+%2B-+sqrt%28+289%29%29%2F2+
x+=+%28-7+%2B17%29%2F2+=5 inches
x+=+%28-7+-17%29%2F2+=-12%3C0 extraneous root
the shortest leg of a triangle is 5 inches, the other leg is 5+7=12 inches