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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
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Solution
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.
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