SOLUTION: The hypotenuse of a right triangle is 15 inches. One of the legs is 3 inches more than the other. Find the lengths of the two legs

Algebra ->  Triangles -> SOLUTION: The hypotenuse of a right triangle is 15 inches. One of the legs is 3 inches more than the other. Find the lengths of the two legs       Log On


   

Question 998545: The hypotenuse of a right triangle is 15 inches. One of the legs is 3 inches more than the other. Find the lengths of the two legs
Found 2 solutions by ikleyn, fractalier:
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E2 + %28x-3%29%5E2 = 15%5E2,

x%5E2+%2B+x%5E2+-+6x+%2B+9 = 225,

2x%5E2+-6x+-+216 = 0,

x%5E2+-+3x+-+108 = 0,

x = 12 and x = -9.

Only positive x suits.

Answer. 12 inches and 12-3 = 9 inches.


Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Call one leg x. The other is x + 3.
Now use the Pythagorean Theorem.
a^2 + b^2 = c^2
x^2 + (x + 3)^2 = 15^2
x^2 + x^2 + 6x + 9 = 225
2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0
Factor this and get
(x+12)(x-9)=0
and x = 9 inches (can't be negative)
x + 3 = 12 inches