Short Answer 
A right-angle triangle has one 90-degree angle and follows Pythagoras’ theorem, which states that the square of the hypotenuse equals the sum of the squares of the other two sides. By applying the theorem, if the hypotenuse is 13 cm and one leg is 5 cm, we find the length of the other leg to be 12 cm.
Step 1: Understanding Right-Angle Triangles
A right-angle triangle is defined as a triangle that contains one 90-degree angle. This type of triangle adheres to the principles of Pythagoras’ theorem, which is fundamental in geometry. The theorem states that in a right triangle, the square of the length of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
Step 2: Applying Pythagoras’ Theorem
To find the length of one side in a right-angle triangle, we can use the formula of Pythagoras’ theorem, expressed as H² = P² + B², where H is the hypotenuse, P is one leg, and B is the other leg. Given that the hypotenuse is 13 cm and one leg is 5 cm, we can rearrange the formula to calculate the unknown side.
- Set up the equation: 13² = 5² + B²
- Solve it: 169 = 25 + B²
- Determine B²: B² = 169 – 25 = 144
Step 3: Calculating the Length of the Third Side
To find the length of the third leg of the triangle, we take the square root of 144, which has been derived from the calculation above. This step finalizes our solution for the length of side B.
- Take the square root: B = ‚à ö144
- Calculate: B = 12 cm
- Conclusion: The third leg of the right-angle triangle measures 12 cm.