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प्रश्न
A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
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उत्तर
Let ABCD be a rhombus having sides AB = BC = CD = DA = x cm
Given that perimeter of a rhombus = 40 cm
`\implies` x + x + x + x = 40
`\implies` 4x = 40
`\implies x = 40/4`
∴ x = 10
In ΔABC, let a = AB = 10 cm, b = BC = 10 cm and c = AC = 12 cm
Now, semi-perimeter of a ΔABC,
`s = (a + b + c)/2`
= `((10 + 10 + 12)/2) cm`
= `32/2 cm`
= 16 cm
∴ Area of ΔABC = `sqrt(s(s - a)(s - b)(s - c))`
= `sqrt(16(16 - 10)(16 - 10)(16 - 12)) cm^2`
= `sqrt(16 xx 6 xx 6 xx 4) cm^2`
= 48 cm2
Now, area of the rhombus ABCD
= 2(Area of ΔABC)
= (2 × 48) cm2
= 96 cm2
∵ Cost of painting the sheet of 1 cm2 = Rs. 5
∴ Cost of painting the sheet of 96 cm2
= Rs. (96 × 5)
= Rs. 480
Thus, the cost of painting the sheet on both sides = Rs. (2 × 480) = Rs. 960
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