Answer :
The cost of painting the triangular board with edges of 6 cm, 8 cm, and 10 cm at the rate of 9 paise per cm2 is calculated using Heron's formula to find the area and then multiplying by the cost per cm2, resulting in Rs. 2.16.The correct answer is option: c.
To calculate the cost of painting a triangular board with edges of 6 cm, 8 cm, and 10 cm at the rate of 9 paise per cm2, we first need to determine the area of the triangle. We can use Heron's formula, which allows us to find the area of a triangle when we know the lengths of all three sides.
Step 1: Calculate the semiperimeter of the triangle
The semiperimeter (s) is half the perimeter of the triangle. The sides are 6 cm, 8 cm, and 10 cm, so the perimeter (p) is 6 + 8 + 10
= 24 cm.
Therefore, the semiperimeter is s
= p/2
= 24/2
= 12 cm.
Step 2: Use Heron's formula to calculate the area
Heron's formula states that the area (A) of a triangle with semiperimeter s and sides a, b, and c is:
A = \/(s(s - a)(s - b)(s - c))
Using the semiperimeter and the sides, the area is:
A = \/(12(12 - 6)(12 - 8)(12 - 10))
= \/(12 \/6 \/4 \/2)
= \/(12\/48)
= \/576
= 24 cm2
Step 3: Calculate the cost of painting
To find the total cost, multiply the area by the cost per cm2, which is 9 paise or 0.09 Rs (because 100 paise = 1 Rs).
Cost = Area \/ Cost per cm2 = 24 cm2 \/ 0.09 Rs/cm2 = 2.16 Rs
Therefore, the cost of painting the triangular board is 2.16 Rs, which corresponds to option c.
