Answer: 
This is 17 to the 1/2 power
The rule is
![\sqrt[n]{x} = x^{1/n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B1%2Fn%7D)
the n is the index of the root. For square roots, n = 2, so,
![\sqrt[n]{x} = x^{1/n}\\\\\sqrt[2]{17} = 17^{1/2}\\\\\sqrt{17} = 17^{1/2}\\](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B1%2Fn%7D%5C%5C%5C%5C%5Csqrt%5B2%5D%7B17%7D%20%3D%2017%5E%7B1%2F2%7D%5C%5C%5C%5C%5Csqrt%7B17%7D%20%3D%2017%5E%7B1%2F2%7D%5C%5C)
If two triangles are similar, that means their side lengths are proportional, so we get the equation

Thus x = 13.6.
Hope that helped!
You’re correct. That’s is the right answer.
By the pythagorean theorem the diagonal length will be:
d^2=x^2+y^2 and since this is a square x=y so
d^2=2x^2 and since d=15
225=2x^2
x^2=112.5
x=√112.5 yds
x≈10.6 yds (to nearest tenth of a yard)