We need to find the value of $x$ in the given figure. The figure consists of two right angles. The lengths of the sides are given as 13, 7, and 4. We need to express the answer in the simplest radical form.

1. Problem Description

We need to find the value of $x$ in the given figure. The figure consists of two right angles. The lengths of the sides are given as 13, 7, and

4. We need to express the answer in the simplest radical form.

2. Solution Steps

First, draw a horizontal line from the top of the segment with length 7 to the left side of the shape. This will create a rectangle at the bottom of the original shape, and a right triangle at the top left.

The height of the new rectangle is 7, and the length of the base is

4. The height of the right triangle is $13 - 7 = 6$.

The length of the base of the right triangle is

4. Let the hypotenuse of this right triangle be $h$.

Using the Pythagorean theorem:

$a^2 + b^2 = c^2$

$6^2 + 4^2 = h^2$

$36 + 16 = h^2$

$52 = h^2$

$h = \sqrt{52} = \sqrt{4 \cdot 13} = 2\sqrt{13}$

The hypotenuse $h$ we found is the value of $x$.

3. Final Answer

$x = 2\sqrt{13}$