SOLUTION: The hypotenuse of a right triangle is 4 cm. longer than the one leg and 18 cm. longer than the other leg. Find the length of each side of the triangle.

Question 38788: The hypotenuse of a right triangle is 4 cm. longer than the one leg and 18 cm. longer than the other leg. Find the length of each side of the triangle.
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the shortest leg x.
The hypotenuse is x + 18.
The other leg is x + 14 since it is only 4 less than the hypotenuse.
Now apply the Pythagorean Theorem: a^2 + b^2 = c^2 and we get
x^2 + (x + 14)^2 = (x + 18)^2
x^2 + x^2 + 28x + 196 = x^2 + 36x + 324
now collecting and solving we get
x^2 - 8x - 128 = 0
(x - 16)(x + 8) = 0
x = 16 or x = -8
but distance is never negative so the short leg is 16 and the longer leg is 30. The hypotenuse is 34.
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