Refer to the attached image. The figure is not to scale. Notice how I've added in y and z (blue and red respectively) The length y is the bottom horizontal leg for the triangle on the right. The length z is the bottom horizontal leg for the triangle on the left.
To find x, we need to find y first, which will help us find z, and then we can finally get to x.
Let's find y first To do this, we use the pythagorean theorem a^2 + b^2 = c^2 y^2 + 9^2 = 15^2 y^2 + 81 = 225 y^2 + 81-81 = 225-81 y^2 = 144 sqrt(y^2) = sqrt(144) y = 12 ... keep in mind that y is a length, so it needs to be positive
Notice how the y and z lengths combine to form a total length of 25 units Therefore, y+z = 25 12+z = 25 12+z-12 = 25-12 z = 13
Now that we know z = 13, we can find x. Again we use the pythagorean theorem one last time a^2 + b^2 = c^2 z^2 + 9^2 = x^2 13^2 + 9^2 = x^2 169 + 81 = x^2 250 = x^2 x^2 = 250 sqrt(x^2) = sqrt(250) x = sqrt(250) x = sqrt(25*10) x = sqrt(25)*sqrt(10) x = 5*sqrt(10) This is in simplest radical form as we can't factor 10 any further (there are no perfect square factors that go into 10). This is the exact length of side x
Note: using a calculator, 5*sqrt(10) = 15.8113883008419 approximately
