Pythagoras Worksheet - GCSE Maths [FREE] - Third Space Learning - Free Printable

I'll solve this problem by applying the Pythagorean Theorem to find the missing side lengths of each right triangle. The Pythagorean Theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse (the longest side opposite the right angle) and a and b are the other two sides.

Let me go through each triangle one by one:

Triangle 1:
- Given: one leg = 6, hypotenuse = 10
- Find: other leg
- Using Pythagorean Theorem: x² + 6² = 10²
- x² + 36 = 100
- x² = 64
- x = 8

Triangle 2:
- Given: one leg = 5, hypotenuse = 13
- Find: other leg
- Using Pythagorean Theorem: x² + 5² = 13²
- x² + 25 = 169
- x² = 144
- x = 12

Triangle 3:
- Given: one leg = 7, hypotenuse = 14
- Find: other leg
- Using Pythagorean Theorem: x² + 7² = 14²
- x² + 49 = 196
- x² = 147
- x = √147 = 7√3 ≈ 12.12

Triangle 4:
- Given: one leg = 21, hypotenuse = 29
- Find: other leg
- Using Pythagorean Theorem: x² + 21² = 29²
- x² + 441 = 841
- x² = 400
- x = 20

Triangle 5:
- Given: both legs = 7
- Find: hypotenuse
- Using Pythagorean Theorem: 7² + 7² = x²
- 49 + 49 = x²
- 98 = x²
- x = √98 = 7√2 ≈ 9.90

Triangle 6:
- Given: one leg = 22, hypotenuse = 26
- Find: other leg
- Using Pythagorean Theorem: x² + 22² = 26²
- x² + 484 = 676
- x² = 192
- x = √192 = 8√3 ≈ 13.86

Triangle 7:
- Given: one leg = 12, hypotenuse = 20
- Find: other leg
- Using Pythagorean Theorem: x² + 12² = 20²
- x² + 144 = 400
- x² = 256
- x = 16

Triangle 8:
- Given: one leg = 12, hypotenuse = 15
- Find: other leg
- Using Pythagorean Theorem: x² + 12² = 15²
- x² + 144 = 225
- x² = 81
- x = 9

Triangle 9:
- Given: one leg = 17, hypotenuse = 18
- Find: other leg
- Using Pythagorean Theorem: x² + 17² = 18²
- x² + 289 = 324
- x² = 35
- x = √35 ≈ 5.92

Triangle 10:
- Given: one leg = 8, hypotenuse = 17
- Find: other leg
- Using Pythagorean Theorem: x² + 8² = 17²
- x² + 64 = 289
- x² = 225
- x = 15

The completed answers for each triangle are:
1. 8
2. 12
3. 7√3 (or approximately 12.12)
4. 20
5. 7√2 (or approximately 9.90)
6. 8√3 (or approximately 13.86)
7. 16
8. 9
9. √35 (or approximately 5.92)
10. 15