The hypotenuse of a right-angled triangle with side lengths of $11 \, \text{cm}$ and $60 \, \text{cm}$ is approximately $61 \, \text{cm}$.

To determine the hypotenuse of a right-angled triangle, we apply Pythagoras’ Theorem. This theorem posits that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship can be expressed mathematically as:

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

In this formula, $c$ represents the hypotenuse, while $a$ and $b$ denote the lengths of the other two sides.

For our triangle, we have side lengths of $11 \, \text{cm}$ and $60 \, \text{cm}$. Substituting these values into the equation yields:

$c^2 = 11^2 + 60^2$ $c^2 = 121 + 3600$ $c^2 = 3721$

Next, to find the length of the hypotenuse $c$, we take the square root of $3721$:

$c = \sqrt{3721}$ $c \approx 61$

Thus, the hypotenuse measures approximately $61 \, \text{cm}$. This method is invaluable for solving problems related to right-angled triangles and is a fundamental concept in GCSE Mathematics. Always remember to verify that the triangle is right-angled before applying Pythagoras’ Theorem.