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Pythagorean theorem: find a leg worksheets

Finding a leg runs the theorem backward: the hypotenuse squared minus the known leg squared, then a square root. These free printable worksheets drill that case alone, cut from the mixed page.

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Pythagorean theorem: find a leg
Pythagorean theorem: find a leg 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

The mixed Pythagorean page mixes finding a leg with finding the hypotenuse, and telling them apart is where children slip: they add when they should subtract. This sheet asks only for a leg, so the subtraction step becomes the habit before the two are combined.

Why this sheet works

Every triangle is built from a Pythagorean triple — 3-4-5, 5-12-13, 8-15-17 and their multiples — so the missing leg is always a whole number and a child practices the method rather than a messy square root. The right angle is marked, and the hypotenuse is the side opposite it, which is the side to square first.

How this one works

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

Right triangle, 20 and 12

121620
  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 given — 20 cm — and a LEG is missing. That is the case where the sum is a subtraction, not an addition.
  3. Square the two you have: 20² = 400 and 12² = 144.
  4. The leg's square is what is LEFT when you take the other leg's square off the hypotenuse's: 400 − 144 = 256.
  5. That is the square, not the side. Take the square root: √256 = 16 cm.

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