SOLUTION: The hypotenuse of a right triangle is 32 feet long. One leg is 2 feet longer than the other. Find the length of the shorter leg. Round your answer to the nearest hundredth.

Algebra ->  Triangles -> SOLUTION: The hypotenuse of a right triangle is 32 feet long. One leg is 2 feet longer than the other. Find the length of the shorter leg. Round your answer to the nearest hundredth.      Log On


   

Question 330992: The hypotenuse of a right triangle is 32 feet long. One leg is 2 feet longer than the other. Find the length of the shorter leg. Round your answer to the nearest hundredth.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this:
Let x be the length of the shorter leg and x+2 be the length of the other leg.
Applying the Pythagorean theorem, we get:
32%5E2+=+x%5E2%2B%28x%2B2%29%5E2 Simplify.
1024+=+2x%5E2%2B4x%2B4 Subtract 1024 from both sides.
2x%5E2%2B4x-1020+=+0 Divide both sides by 2 to simplify a bit.
x%5E2%2B2x-510+=+0 Solve this by the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a where: a = 1, b = 2, and c = -510
x+=+%28-2%2B-sqrt%282%5E2-4%281%29%28-510%29%29%29%2F2%281%29
You can work this out on your calculator and you should get:
x+=+-23.605 and x+=+21.605 Discard the negative solution, and your answer is:
x+=+21.61Rounded to the nearest hundredth.