What is the hypotenuse of a right-angled triangle with sides 5 cm and 12 cm?

The hypotenuse of a right-angled triangle with sides 5 cm and 12 cm is 13 cm.

To find the hypotenuse of a right-angled triangle, we use Pythagoras' Theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, this is written as \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides.

In this case, the sides of the triangle are 5 cm and 12 cm. Let's denote these sides as \(a = 5\) cm and \(b = 12\) cm. According to Pythagoras' Theorem, we need to calculate \(c\) using the formula:

\[c^2 = a^2 + b^2\]

Substituting the given values:

\[c^2 = 5^2 + 12^2\]
\[c^2 = 25 + 144\]
\[c^2 = 169\]

To find \(c\), we take the square root of 169:

\[c = \sqrt{169}\]
\[c = 13\]

Therefore, the hypotenuse of the triangle is 13 cm. This method is a fundamental part of GCSE Maths and is essential for solving problems involving right-angled triangles. Remember, always ensure your triangle is right-angled before applying Pythagoras' Theorem.