We are asked to find the value of $x$ in the given figure. The figure shows two right triangles sharing a common side. We need to express the answer in the simplest radical form.

1. Problem Description

We are asked to find the value of $x$ in the given figure. The figure shows two right triangles sharing a common side. We need to express the answer in the simplest radical form.

2. Solution Steps

Let the length of the common side be $y$.

For the smaller right triangle, using the Pythagorean theorem, we have

$4^2 + 6^2 = y^2$

$16 + 36 = y^2$

$y^2 = 52$

For the larger right triangle, using the Pythagorean theorem, we have

$x^2 + y^2 = 9^2$

$x^2 + 52 = 81$

$x^2 = 81 - 52$

$x^2 = 29$

$x = \sqrt{29}$

3. Final Answer

$x = \sqrt{29}$