Question

Study the layout given in the following figure and answer the questions:

1. Write an expression for the total area covered by both the bedrooms and the kitchen.
2. Write an expression to calculate the perimeter of the living room.
3. If the cost of carpeting is ₹ 50/m², write an expression for calculating the total cost of carpeting both the bedrooms and the living room.
4. If the cost of tiling is ₹ 30/m², write an expression for calculating the total cost of floor tiles used for the bathroom and kitchen floors.
5. If the floor area of each bedroom is 35 m², then find x.

Answer 1

a. Area of both bedrooms and the kitchen = (Area of bedroom) × 2 + Area of kitchen

= (5 × x)2 + 15 – (x + 2) × 5

= 10x + (75 – 5x – 10)

= 10x + 65 – 5x

= (65 + 5x) m²

b. Perimeter of the living room = 15 + 2 + 5 + (15 – x) + 5 + x + 2 = 44 m 

c. Total area of both the bedrooms and the living room = 5x × + 7 × 15 = (5x + 105) m²

∴ Total cost of carpeting = (5x + 105) × 50 = ₹ 250(x + 21)

d. Total area of bathroom and kitchen = (15 – x) × 5 m²

∴ Total cost of tiling = (15 – x) × 5 × 30 = ₹ 150(15 – x)

e.  Given, area of floor of each bedroom = 35 m²

Area of one bedroom = 5x m²

∴ 5x = 35

⇒ x = 7 m