Find the hypotenuse of a right triangle with legs 5 cm and 12 cm.

13 cm

By Pythagoras theorem: h² = 5² + 12² = 25 + 144 = 169, so h = √169 = 13 cm. This is the famous 5-12-13 Pythagorean triple.

Understanding Geometry questions

Geometry questions reward a quick sketch. Marking the given lengths and angles on a diagram usually reveals which formula or theorem applies before you do any arithmetic.

How to approach it

1. Draw the figure and label every given measurement.
2. Identify the shape family — triangle, quadrilateral, circle or solid.
3. Recall the matching area, perimeter, surface-area or volume formula.
4. Substitute and keep the correct square or cubic units in the answer.

Common mistakes to avoid

• Using slant height where perpendicular height is required.
• Reporting area in linear units instead of square units.
• Forgetting that π ≈ 22/7 and 3.14 give slightly different answers.

Where it appears: Appears in CBSE Class 6–10, IGCSE Core and Extended, and Common Core geometry strands.