using pythagorean theorem
a^2 + b^2 = c^2
(12x)^2 + (16x)^2 = 10^2
square each term
144x^2 + 256x^2 = 100
combine like terms
400 x^2 = 100
divide by 400 on each side
x^2 = 1/4
take the square root on each side
x = 1/2
Answer: x=1/2
