In a right-angled triangle, hypotenuse is 10 cm and the ratio of the other two sides is 3 : 4, the sides are :

1. 6 cm and 4 cm

2. 8 cm and 6 cm

3. 3 cm and 4 cm

4. 8 cm and 4 cm

Given,

Hypotenuse is 10 cm and the ratio of the other two sides is 3 : 4.

Let other two sides be 3x and 4x.

By pythagoras theorem,

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

⇒ 10² = (3x)² + (4x)²

⇒ 100 = 9x² + 16x²

⇒ 100 = 25x²

⇒ x² = $\dfrac{100}{25}$

⇒ x² = 4

⇒ x = $\sqrt{4} = \pm 2$.

Since, side cannot be negative.

∴ x = 2.

⇒ 3x = 3(2) = 6 cm and 4x = 4(2) = 8 cm.

Hence, Option 2 is the correct option.