Quick answer: A triangle is right-angled if the square of its largest side equals the sum of the squares of the other two sides. First ensure the lengths form a triangle.
Worked example
Are 7 cm, 24 cm and 25 cm the sides of a right triangle?
- Triangle inequality holds: 7 + 24 > 25.
- The largest side is 25, so compare 25² with 7² + 24².
- 625 = 49 + 576 = 625.
- Therefore the triangle is right-angled, opposite the 25 cm side.
Check the result
The squared lengths match exactly; an approximate visual drawing is unnecessary.
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Common mistake to avoid
Never choose the first listed side as hypotenuse automatically. Lengths 1, 2, 3 do not form a nondegenerate triangle.
Try it yourself
1. Test 6, 8, 10. 2. Test 5, 6, 7.
Answers and reasoning
1. 100 = 36 + 64, so right-angled. 2. 49 ≠ 25 + 36, so not right-angled.
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