What is the length of the hypotenuse if the legs are 5 cm and 12 cm?

The length of the hypotenuse is 13 cm.

To find the length of the hypotenuse in a right-angled triangle when the lengths of the other two sides (the legs) are known, we use the Pythagorean theorem. The Pythagorean 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 expressed as \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs.

In this case, the lengths of the legs are 5 cm and 12 cm. Plugging these values into the Pythagorean theorem, we get:
\[5^2 + 12^2 = c^2\]
\[25 + 144 = c^2\]
\[169 = c^2\]

To find \(c\), we take the square root of both sides:
\[c = \sqrt{169}\]
\[c = 13\]

Therefore, the length of the hypotenuse is 13 cm. This method is a fundamental part of GCSE Maths and is very useful for solving problems involving right-angled triangles. Remember, the Pythagorean theorem only applies to right-angled triangles, so always ensure the triangle in question has a right angle before using this method.