It seems you've uploaded a mathematical image related to a triangle and asking for the value of $x$. Let me carefully analyze the image to extract the necessary information and solve for $x$.

Give me a moment to process this.I see that this is a geometry problem involving a triangle $ABC$ with points $B$, $C$, and $D$. From the information provided:

• $AB = 20$
• $AC = 15$
• $BC = 25$
• $AD = x$
• The triangle is right-angled at $D$.

We can use the Pythagorean theorem to solve for $x$, as the triangle $ACD$ is a right triangle. According to the Pythagorean theorem:

$AC^2 + AD^2 = CD^2$

Substituting the known values:

$15^2 + x^2 = 25^2$ $225 + x^2 = 625$

Now, solving for $x^2$:

$x^2 = 625 - 225$ $x^2 = 400$

Taking the square root of both sides:

$x = \sqrt{400} = 20$

So, the value of $x$ is 20.

Would you like further clarification on any part of the solution, or do you have other questions related to this?

Here are some related questions that might help deepen your understanding:

1. How does the Pythagorean theorem apply in other geometric shapes?
2. How can we solve for the hypotenuse of a right triangle using the Pythagorean theorem?
3. What is the difference between a right triangle and an isosceles triangle?
4. How do you apply trigonometry to find unknown sides in right triangles?
5. What happens when you use the Pythagorean theorem in 3D geometry?

Tip: Always check if the triangle is a right triangle first before applying the Pythagorean theorem!