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Question
Study the layout given in the figure and answer the questions:
- Write an expression for the total area covered by both the bedrooms and the kitchen.
- Write an expression to calculate the perimeter of the living room.
- 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.
- 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.
- If the floor area of each bedroom is 35 m2, then find x.
Solution
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
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