Statement 1: The side of a triangular board are 8 cm, 6 cm and 10 cm; the cost of painting it at the rate of ₹ 10 per square cm is $\dfrac{1}{2}$ x 6 x 8 x ₹ 10.

Statement 2: 10² = 8² + 6²

⇒ Sides of the triangle are 8 cm and 6 cm.

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Given,

Sides of a triangular board are 8 cm, 6 cm and 10 cm.

⇒ 10² = 100, 8² = 64 and 6² = 36.

⇒ 100 = 64 + 36

⇒ 10² = 8² + 6²

This confirms the triangle with sides 6 cm, 8 cm, and 10 cm is a right triangle, where 10 cm is the hypotenuse.

Thus, sides of the triangle are 8 cm and 6 cm.

So, statement 2 is true.

Area of triangle = $\dfrac{1}{2}$ x base x height

= $\dfrac{1}{2}$ x 8 x 6

Rate of painting = ₹ 10 per square cm

Cost of painting = Area x rate of painting

= $\dfrac{1}{2}$ x 8 x 6 x ₹ 10

So, statement 1 is true.

∴ Both the statements are true.

Hence, option 1 is the correct option.