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The problem you're dealing with involves the Pythagorean theorem, which is used to find the length of the sides of a right-angled triangle. Given that the two short sides of the right-angled triangle have lengths \( L_1 \) and \( L_2 \), you need to express the length of the third side, \( L_3 \), in terms of \( L_1 \) and \( L_2 \).

For a right-angled triangle, the Pythagorean theorem states:

\[
L_3^2 = L_1^2 + L_2^2
\]

To express \( L_3 \), take the square root of both sides:

\[
L_3 = \sqrt{L_1^2 + L_2^2}
\]

So, the length of the third side, \( L_3 \), is given by:

\[
L_3 = \sqrt{L_1^2 + L_2^2}
\]

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. How would the equation change if \( L_3 \) was one of the shorter sides?
2. Can you apply the Pythagorean theorem in three dimensions for a rectangular prism?
3. What happens to the value of \( L_3 \) if both \( L_1 \) and \( L_2 \) are doubled?
4. How would you find the length of the hypotenuse if you knew the lengths of \( L_3 \) and \( L_1 \)?
5. Could this formula be used to verify if a given triangle is a right triangle?

**Tip:** The Pythagorean theorem is only applicable to right-angled triangles. If you encounter a triangle without a right angle, you'll need to use other methods, such as the Law of Cosines, to find the length of a side.

The two short sides of a right-angled triangle have lengths L1 and L2. Express the length of the third side, L3, in terms of L1 and L2.

Learn how to find the length of the hypotenuse in a right-angled triangle using the Pythagorean theorem. This guide covers the formula L3 = √(L1² + L2²) and provides a step-by-step explanation suitable for students in Grades 7-10.

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