First we need to find y It turns out we can set up the proportion 4/y = y/12 since the two inner smaller triangles are similar triangles
Solve for y by cross multiplying 4/y = y/12 4*12 = y*y 48 = y^2 y^2 = 48 y = sqrt(48)
Now use this y value to find x Use the pythagorean theorem. Focus on the smaller triangle on the right side a^2 + b^2 = c^2 y^2 + 12^2 = x^2 (sqrt(48))^2 + 12^2 = x^2 48 + 144 = x^2 192 = x^2 x^2 = 192 x = sqrt(192) x = sqrt(64*3) x = sqrt(64)*sqrt(3) x = 8*sqrt(3)
