Legs 6 and 8
- Input
- a=6, b=8
- Expected output
- c=10
c²=36+64=100; the (6,8,10) triple is exactly double (3,4,5), so the result comes out whole.
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find the hypotenuse
The hypotenuse is a right triangle's longest side, always opposite the 90° angle, and it comes from adding the squares of the two legs: c=√(a²+b²). Unlike computing a leg, the operation inside the root here is always an addition, never a subtraction, so any pair of positive legs has a solution.
c²=36+64=100; the (6,8,10) triple is exactly double (3,4,5), so the result comes out whole.
c²=3,686,400+1,166,400=4,852,800; the diagonal in pixels does not match the measurement in inches without the panel's pixel density.
2.5, 6 and 6.5 are the (5,12,13) triple divided by 2, which is why the result comes out exact, with no repeating decimal.
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: c² = a² + b². Attributed to Greek mathematician Pythagoras (~570–495 BC).
No, never: since c=√(a²+b²) adds two positive values inside the root, c is always larger than a and larger than b on their own. For a=6 and b=8, for example, c=10 is larger than both legs that produced it.
Yes: width and height act as the two legs, and the diagonal is the hypotenuse. A 1920×1080 pixel screen has a diagonal of about 2202.91 pixels; converting that to inches still requires dividing by the panel's pixels-per-inch density.
Because not every pair of legs forms an exact Pythagorean triple: only specific combinations, like (6,8,10) or (5,12,13), give three whole-number sides at once. Outside those combinations, the square root of a²+b² is an irrational number, shown as an approximate decimal.
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