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Is It a Right Triangle? Checker

Solve a² + b² = c² step by step: find the hypotenuse from two legs, find a missing leg, or test whether three sides form a right triangle — with exact simplified radicals like 5√2, a scaled diagram, area and perimeter.

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Validating sides
Substituting into the theorem
Simplifying the square root
Done

Result

This page opens the Pythagorean theorem calculator in check mode: enter any three sides and the converse of the theorem is applied — the longest side is treated as the hypotenuse and a² + b² = c² is evaluated exactly. For 5, 12, 13 the check reads 25 + 144 = 169 = 13², so the answer is yes; for 6, 7, 8 the sums disagree and the answer is an honest no.

The comparison is done on exact scaled integers, not floating-point approximations, so decimal side lengths are judged correctly and near-misses are never rounded into false positives. The full computation is printed in both the yes and the no case, and a confirmed right triangle also gets its area, perimeter and a scaled diagram.

Builders know this test as the 3-4-5 rule for squaring corners, and the same check verifies Pythagorean triples like 8-15-17 or 20-21-29 in seconds. If your triangle turns out not to be right-angled, the general triangle calculator on this site will still solve all of its angles from the three sides via the law of cosines.

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Accepted Formats & Rules

  • Three modes: find the hypotenuse from two legs, find a missing leg from a leg and the hypotenuse, and check whether three sides make a right triangle.
  • Exact arithmetic on decimal inputs and exact simplified radicals (c = 5√2) next to rounded decimals.
  • Also computes the area and perimeter of the triangle and draws it with the right angle marked.

Key Benefits

✓ Every answer shows the full a² + b² = c² substitution, so the working is ready to copy into homework.
✓ Irrational results are given exactly — √50 is simplified to 5√2 by integer factorization — alongside the decimal value.
✓ Runs entirely in your browser: no sign-up, no uploads, instant results with a right-triangle diagram scaled to your sides.

Use Cases

  • • Find the hypotenuse from two legs with the full a² + b² = c² substitution — 3 and 4 give √25 = 5, ready for homework.
  • • Get a missing side as an exact simplified radical: legs of 5 and 5 return 5√2 ≈ 7.0711, never just a rounded decimal.
  • • Check whether sides like 5, 12, 13 form a right triangle with the squares compared exactly and the computation shown.