SOLUTION: If the length of one leg in a right triangle is three times the length of the other and the hypotenuse is 20, find the length of the shorter leg. I know it's somewhere between 6-7.

Algebra ->  Triangles -> SOLUTION: If the length of one leg in a right triangle is three times the length of the other and the hypotenuse is 20, find the length of the shorter leg. I know it's somewhere between 6-7.      Log On


   

Question 293605: If the length of one leg in a right triangle is three times the length of the other and the hypotenuse is 20, find the length of the shorter leg. I know it's somewhere between 6-7. Please show me how to solve it as well!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
short leg is x, so long leg is 3x

by Pythagoras ___ x^2 + (3x)^2 = 20^2

x^2 + 9x^2 = 400 ___ 10x^2 = 400 ___ x^2 = 40 ___ x = sqrt(40) ___ between 6 and 7