This is a right triangle where:

• One leg is 20 units,
• The hypotenuse is 25 units, and
• The remaining side, denoted as $x$, is what we need to find.

We can use the Pythagorean Theorem to solve for $x$. The theorem states:

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

where $a$ and $b$ are the legs of the right triangle, and $c$ is the hypotenuse.

Here:

• $a = 20$ (one leg),
• $b = x$ (the other leg),
• $c = 25$ (the hypotenuse).

Now, applying the Pythagorean Theorem:

$20^2 + x^2 = 25^2$

This simplifies to:

$400 + x^2 = 625$

Now, solve for $x^2$:

$x^2 = 625 - 400 = 225$

Finally, take the square root of both sides:

$x = \sqrt{225} = 15$

Thus, the value of $x$ is $\boxed{15}$.

Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:

1. What is the length of the hypotenuse if both legs are 9 and 12?
2. If one leg is 7 and the hypotenuse is 25, what is the length of the other leg?
3. Can a triangle with sides 10, 24, and 26 be a right triangle?
4. What is the area of a right triangle with legs 8 and 15?
5. How does the Pythagorean theorem relate to the distance formula in coordinate geometry?

Tip: Always double-check units and values when applying the Pythagorean theorem to avoid small calculation errors.