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Pythagorean theorem: find the hypotenuse worksheets

The hypotenuse is the longest side of a right triangle: square the two legs, add them, then take the square root. These free printable worksheets drill that case alone, cut from the mixed page.

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Pythagorean theorem: find the hypotenuse
Pythagorean theorem: find the hypotenuse worksheet — Pythagorean triples, sides to 70 cm, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

This is the forward direction of the theorem, split from the mixed page where it is interleaved with finding a leg. Facing only hypotenuse questions lets a child fix the add step cleanly before having to decide, on a mixed sheet, whether to add or subtract.

Why this sheet works

Every triangle is drawn from a Pythagorean triple and its multiples, so the two legs always give a whole-number hypotenuse — a thirteen-year-old practices the theorem, not the square root of 41 crammed into a blank the width of a number. The right angle is marked, and the missing side is always the one opposite it.

How this one works

One question from this sheet, worked through a step at a time.

Right triangle, 3 and 4

34?
  1. The hypotenuse is the side OPPOSITE the right angle — never one of the two that make the corner. It is also always the longest, so you can check yourself twice.
  2. Here the hypotenuse is the missing one, so the two given sides are both legs: 3 and 4.
  3. Square the two you have: 3² = 9 and 4² = 16.
  4. The two squares ADD to the square on the hypotenuse: 9 + 16 = 25.
  5. That is the square, not the side. Take the square root: √25 = 5 cm.

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