Study the layout given below in Fig. and answer the questions: a.… - Vidyadip

Question

Study the layout given below in Fig. and answer the questions:

$a.$ Write an expression for the total area covered by both the bedrooms and the kitchen.
$b.$ Write an expression to calculate the perimeter of the living room.
$c.$ If the cost of carpeting is $Rs. 50/m^2,$ write an expression for calculating the total cost of carpeting both the bedrooms and the living room.
$d.$ If the cost of tiling is $Rs. 30/m^2,$ write an expression for calculating the total cost of floor tiles used for the bathroom and kitchen floors.
$e.$ If the floor area of each bedroom is $35m^2,$ then find $x.$

✓

Answer

$a.$ Area of both bedroom and the kitchen $=($ Area of bedroom $) \times 2+$ Area of kitchen
$=(5 \times x) 2+15-(x+2) \times 5$
$=10 x+(75-5 x-10)$
$=10 x+65-5 x$
$=(65+5 x) \mathrm{m}^2$
$b.$ Perimeter of the living room $=15+2+5+(15-x)+5+x+2=44 \mathrm{~m}$
$c.$ Total area of both the bedrooms and the living room $=5 \times x+7 \times 15=(5 x+105) \mathrm{m}^2$
$\therefore$ Total cost of carpeting $=(5 x+105) \times 50= Rs. 250(x+21)$
$d.$ Total area of bathroom and kitchen $=(15-\mathrm{x}) \times 5 \mathrm{~m}^2$
$\therefore$ Total cost of tiling $=(15-\mathrm{x}) \times 5 \times 30= Rs. 150(15-\mathrm{x})$
$e.$ Given, area of floor of each bedroom $=35 \mathrm{~m}^2$
Area of one bedroom $=5\ \mathrm{xm}^2$
$\therefore 5 x=35$
$\Rightarrow x=7 m$

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