Question

Anybody know the answer?

Answer 1

I'd start by writing an equation for each of the right triangles. (Pythagorean theorem)

y² + 9² = z²
x² + z² = (4+9)²
4² + y² = x²

we want to find z so combine the equations by substituting the other variables x,y out.

substitute y² for (x² - 4²) in 1st equation.

(x² - 4²) + 9² = z²

now by rearranging the 2nd equation we can substitute x² for (13² - z²)

(13² - z²) - 4² + 9² = z²
169 - z² - 16 + 81 = z²
234 - z² = z²
234 = 2z²
234/2 = z²
117 = z²
√(117) = z
√(9*13) = z
3√(13) = z

13 goes in the box