Question

A rhombus sheet whose perimeter is 40 m and whose one diagonal is 12 m long. Find the cost of painting both side of the sheet at the rate of Rs 7 per m².

1. Rs. 1345
2. Rs. 1367
3. Rs. 1455
4. Rs. 1344

Answer 1

Correct Answer - Option 4 : Rs. 1344

Given:

Perimeter of Rhombus = 40 m

Diagonal = 12 m

Rate of painting = 7 per m2

Formula used:

Perimeter of Rhombus = 4 × side

Area of Rhombus = (d1 × d2)/2

Area of Rhombus = Side × Altitude

d12 + d22 = 4 × s2

Here, d1, d2, and s are diagonals and side of rhombus respectively.

Concept used:

All sides of a rhombus are equal and diagonals bisect each other at a right angle.

Calculation:

Perimeter of Rhombus = 4 × side

⇒ 40 = 4 × side

⇒ side = 10 m

Now, d12 + d22 = 4 × s2

⇒ 122 + d22 = 4 × 102

⇒ d22 = 256

⇒ d2 = 16

Now, Area of Rhombus = (d1 × d2)/2

⇒ Area = (12 × 16)/2 = 96 m2

Area of both sides of sheet = 2 × 96 m2 = 192 m2

Cost of painting = 7 × 192 = 1344

∴ Cost of painting both side of sheet is Rs. 1344