PREVIOUSLY ASKED IN:
CTET 2026
Answer
8, 16, 12
Explanation
The sides of a right triangle must satisfy the Pythagorean theorem: \( a^2 + b^2 = c^2 \) (where c is the longest side). Option 1: \( 12^2 + 16^2 = 144 + 256 = 400 = 20^2 \) (Valid). Option 2: \( 4.5^2 + 6^2 = 20.25 + 36 = 56.25 = 7.5^2 \) (Valid). Option 3: \( 8^2 + 12^2 = 64 + 144 = 208 \), but \( 16^2 = 256 \). 208 ≠ 256 (Invalid). Option 4: \( 2.5^2 + 6^2 = 6.25 + 36 = 42.25 = 6.5^2 \) (Valid).
Key Points
- > The Pythagorean theorem only applies to right-angled triangles.
- > The longest side must always be considered the Hypotenuse.
- > A set of three integers that satisfy the theorem is called a Pythagorean Triplet.
- > Multiplying or dividing a Pythagorean triplet by a constant yields another valid triplet.
- > (E.g., multiplying 3, 4, 5 by 4 gives 12, 16, 20).
- > For decimal values, it's easier to scale them up to integers first (e.g., multiply 4.5, 6, 7.5 by 2 to get 9, 12, 15, which is a multiple of 3, 4, 5).
Additional Information
Common Pythagorean Triplets
| Base Triplet | Multiplied (x2) | Multiplied (x3) | Halved (x0.5) |
|---|---|---|---|
| 3, 4, 5 | 6, 8, 10 | 9, 12, 15 | 1.5, 2, 2.5 |
| 5, 12, 13 | 10, 24, 26 | 15, 36, 39 | 2.5, 6, 6.5 |
| 8, 15, 17 | 16, 30, 34 | 24, 45, 51 | 4, 7.5, 8.5 |
| 7, 24, 25 | 14, 48, 50 | 21, 72, 75 | 3.5, 12, 12.5 |
Memory Tips
- Checking Trick: Always identify the largest number first. Square it. If it doesn't equal the sum of the squares of the other two numbers, it's not a right triangle.