Question

A carpet is spread in a square room leaving a margin of 5 dm all round the carpet. Find the cost of the carpet at ₹ 2.20 per sq. m, if the margin occupies an area of 13 m².

Answer 1

Given: A carpet is spread in a square room leaving a margin of 5 dm all round; the margin area is 13 m². Cost of carpet = ₹ 2.20 per m².

Step-wise calculation:

1. Convert margin width: 5 dm = 0.5 m.

2. Let s = side of the square room (m).

Side of the carpet

= s – 2 × 0.5 

= s – 1 (m)

3. Margin area

= Area of room – Area of carpet 

= s² – (s – 1)²

Compute: s² – (s – 1)²

= s² – (s² – 2s + 1)

= 2s – 1

4. Set margin area = 13:

2s – 1 = 13 

⇒ 2s = 14 

⇒ s = 7 m

5. Carpet side = s – 1

= 7 – 1 

= 6 m 

⇒ Carpet area = 6²

= 36 m²

6. Cost = 36 m² × ₹ 2.20/m²

= ₹ 79.20

The cost of the carpet is ₹ 79.20.