The given image shows a right-angled triangle $\triangle LNZ$, where:

• $\angle L = 90^\circ$
• $LN = x$ (one leg)
• $LZ = 20$ (the other leg)
• $NZ = 25$ (the hypotenuse)

We can use the Pythagorean theorem, which states:

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

Substituting the given values:

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

$x^2 + 400 = 625$

$x^2 = 225$

$x = \sqrt{225} = 15$

So, $x = 15$.

Would you like a step-by-step breakdown of the theorem? Here are some related questions:

1. What is the Pythagorean theorem, and why does it work?
2. How can we use trigonometry (sine, cosine, tangent) to solve for unknown sides?
3. What are Pythagorean triples, and how do they relate to this problem?
4. How can we determine the area of this right-angled triangle?
5. Can this method be applied to non-right-angled triangles?

Tip: Always check whether a given set of three numbers forms a right triangle using the Pythagorean theorem!