Question

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.

Answer 1

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