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Question
The length and the breadth of a conference hall are in the ratio 7: 4 and its perimeter is 110 m. Find:
(i) area of the floor of the hall.
(ii) a number of tiles, each a rectangle of size 25 cm x 20 cm, required for the flooring of the hall.
(iii) the cost of the tiles at the rate of ₹ 1,400 per hundred tiles.
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Solution
Ratio in length and breadth = 7 : 4
Perimeter = 110 m
∴ Length + Breadth = `110/2 = 55` m
Sum of ratios = 7 + 4 = 11
∴ Length = `(55 xx 7)/11 = 35` m
and breath = `(55 xx 4)/11 = 20` m
(i)
Area of floor = l × b
= `35 xx 20 = 700 "m"^2`
(ii)
Size of tile = 25 cm × 20 cm
= `(25 xx 20)/(100 xx 100)`
= `1/20 "m"^2`
∴ Number of tiles
= `"Area of floor"/"Area of one tile"`
= `(700 xx 20)/1 = 14000`
(iii)
Cost of tiles = ₹ 1400 per 100 tiles
∴ Total cost = `(14000 xx 1400)/100`
= ₹ 196000
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