GCSE Maths Practice: pythagoras-theorem

Question 5 of 10

This question asks students to identify the formula for the space diagonal of a cuboid using 3D Pythagoras.

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\( \begin{array}{l}\text{Which formula finds the space diagonal of a cuboid with length } l, \text{ width } w, \text{ and height } h?\end{array} \)

Choose one option:

3D diagonal = √(length² + width² + height²).

To find the space diagonal of a cuboid with length l, width w, and height h, we treat it as a right-angled triangle in 3D. The diagonal forms the hypotenuse, and the three dimensions form the perpendicular sides. Apply Pythagoras' Theorem: d = √(l² + w² + h²). This is an extension of the 2D Pythagoras' Theorem. Understanding this concept is crucial for solving three-dimensional problems, calculating distances across boxes, rooms, or cuboids, and visualising geometric relationships. Practising space diagonal problems builds spatial reasoning, essential for GCSE questions and real-world applications like construction, design, and navigation.