Question

The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 9 paise per cm² is ______.

Options

• Rs 2.00

• Rs 2.16

• Rs 2.48

• Rs 3.00

Answer 1

The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 9 paise per cm² is Rs 2.16.

Explanation: 

Since, the edges of a triangular board area a = 6 cm, b = 8 cm and c = 10 cm.

Now, semi-perimeter of a triangular board,

`s = (a + b + c)/2`

= `(6 + 8 + 10)/2`

= `24/2`

= 12 cm

Now, area of a triangular board = `sqrt(s(s - a)(s - b)(s - c))`  ...[By Heron’s formula]

= `sqrt(12(12 - 6)(12 - 8)(12 - 10))`

= `sqrt(12 xx 6 xx 4 xx 2)`

= `sqrt((12)^2 xx (2)^2)`

= 12 × 2

= 24 cm²

Since, the cost of painting for area 1 cm² = ₹ 0.09

∴ Cost of paint for area 24 cm² = 0.09 × 24 = ₹ 2.16

Hence, the cost of a triangular board is ₹ 2.16.