Example 1 · level 1
A right-angled triangle has legs 21 cm and 72 cm. Find the hypotenuse (in cm).
Show solution
- 21² + 72² = 441 + 5184 = 5625.
- Hypotenuse = √5625 = 75 cm.
Answer: 75 cm
CLASS 7 MATHS · THE TRIANGLE AND ITS PROPERTIES
Pythagoras theorem
In a right triangle, hypotenuse² = base² + height². The hypotenuse is the side opposite the right angle.
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Worked examples
Example 2 · level 2
In a right triangle the hypotenuse is 123 cm and one leg is 27 cm. Find the other leg (in cm).
Show solution
- other² = 123² − 27² = 15129 − 729 = 14400.
- other = √14400 = 120.
Answer: 120 cm
Example 3 · level 3
A 34 m ladder leans against a wall in Kochi. Its foot is 16 m from the wall. How high up the wall does it reach (in m)?
Show solution
- other² = 34² − 16² = 1156 − 256 = 900.
- other = √900 = 30.
Answer: 30 m