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 m'. Find the cost of painting.
(Rs960)​

Answer 1

Let ABCD be a rhombus having each side equal to x cm

i.e., AB = BC = CD = DA = x cm

Given, perimeter of rhombus = 40

∴ AB + BC + CD + DA = 40

⇒ x + x + x + x = 40

⇒ 4x = 40

∴ x = 10 cm

In ∆ABC,

Let a = AB =10 cm, b = BC = 10 cm and c = AC = 12cm

Now, Semi – Perimeter ∆ABC,

= + + /2

  = 10+10+12/2

  = 32/2

= 16

∴ ∆ABC = √( − )( − )( − ) [By Heron’s formula]

= √16(16 − 10)(16 − 10) (16 − 12)

= √16 × 6 × 6 × 4 = 4× 6×2 = 482

therefore on both sides= 48×2=96cm²

Cost of painting of the sheet of 1 2 = Rs 5

∴ Cost of painting of the sheet of 96 2 = 96×5 = Rs480

Hence, the cost of the painting of the sheet for both sides = 2×480 = Rs 960