Question

Which of the sides can not form a right-angled Δ?

Options

• 6, 8, 10

• 4.5, 6, 7.5

• 9, 12, 15

• 8, 13, 15

Answer 1

8, 13, 15

Explanation:

Let’s check each option using the Pythagoras theorem:

For a right-angled triangle,

(Hypotenuse)² = (Base)² + (Perpendicular)²

⇒ Option 6, 8, 10:

Largest side = 10

10² = 6² + 8²

100 = 36 + 64

100 = 100

Forms a right-angled triangle.

⇒ Option 4.5, 6, 7.5:

Largest side = 7.5

7.5² = 4.5² + 6²

56.25 = 20.25 + 36

56.25 = 56.25

Forms a right-angled triangle.

⇒ Option 9, 12, 15:

Largest side = 15

15² = 9² + 12²

225 = 81 + 144

225 = 225

Forms a right-angled triangle.

⇒ Option 8, 13, 15:

Largest side = 15

15² = 8² + 13²

225 = 64 + 169

225 ≠ 233

∴ 8, 13, 15 cannot form a right-angled triangle.