SOLUTION: Joe cuts out a piece of paper in the shape of a right triangle. The longer leg of the triangle is 20 inches longer than twice the length of the shorter leg. The hypotenuse is 30 in

Algebra ->  Pythagorean-theorem -> SOLUTION: Joe cuts out a piece of paper in the shape of a right triangle. The longer leg of the triangle is 20 inches longer than twice the length of the shorter leg. The hypotenuse is 30 in      Log On


   

Question 1186317: Joe cuts out a piece of paper in the shape of a right triangle. The longer leg of the triangle is 20 inches longer than twice the length of the shorter leg. The hypotenuse is 30 inches longer than twice the length of the shorter leg. What is the length of the longer leg?
Found 2 solutions by greenestamps, robertb:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Response removed -- I read the given information incorrectly

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!

Shorter leg = x
Longer leg = 2x + 20
Hypotenuse = 2x + 30

===> x%5E2+%2B+%282x%2B20%29%5E2+=+%282x%2B30%29%5E2 ===> x%5E2+-+40x+-+500+=+0 after expanding some terms and simplifying.
<===> (x-50)(x+10) = 0. ===> x = 50. (x = -10 is not acceptable.)
===> The length of the longer leg is 2*50 + 20 = 120 inches.