🔺 Pythagorean Theorem Explorer

The Pythagorean Theorem

c² = a² + b²

In a right triangle, the square of the hypotenuse (c) is equal to the sum of squares of the other two sides (a and b).

Part I: Solving for Missing Values

Problem 1: Given a = 3, b = 5

c² = 3² + 5²
c² = 9 + 25
c² = 34
c = √34 ≈ 5.83

Problem 2: Given b = 9, c = 20

a² + 9² = 20²
a² + 81 = 400
a² = 319
a = √319 ≈ 17.86

Problem 3: Given b = 9, c = 15

a² + 9² = 15²
a² + 81 = 225
a² = 144
a = 12

Problem 4: Given a = 18, b = 30

c² = 18² + 30²
c² = 324 + 900
c² = 1224
c = √1224 ≈ 34.99

Problem 5: Given b = 6, c = 20

a² + 6² = 20²
a² + 36 = 400
a² = 364
a = √364 ≈ 19.08

Part II: Verifying Pythagorean Triples

Case 1: 20, 21, 29

20² + 21² = 29²
400 + 441 = 841
✓ True

Case 2: 8, 6, 10

8² + 6² = 10²
64 + 36 = 100
✓ True

Case 3: 16, 7, 56

16² + 7² ≠ 56²
256 + 49 ≠ 3136
✗ False

Case 4: 3, 4, 5

3² + 4² = 5²
9 + 16 = 25
✓ True

Case 5: 16, 65, 63

16² + 65² ≠ 63²
256 + 4225 ≠ 3969
✗ False