The length of a hall is 18 m and its width is 13.5 m. Find the least number of square tiles, each of side 25 cm, required to cover the floor of the hall,
(i) without leaving any margin.
(ii) leaving a margin of width 1.5 m all around.
In each case, find the cost of the tiles required at the rate of ₹ 6 per tile.

Question

The length of a hall is 18 m and its width is 13.5 m. Find the least number of square tiles, each of side 25 cm, required to cover the floor of the hall,
(i) without leaving any margin.
(ii) leaving a margin of width 1.5 m all around.
In each case, find the cost of the tiles required at the rate of ₹ 6 per tile.

KnowledgeBoat · Accepted Answer

(i) Given: Length of the floor = 18 m Breadth of the floor = 13.5 m As we know, the area of the floor = length x breadth = 18 x 13.5 m² = 243 m² Side of the square tile = 25 cm = m = m As we know, the area of a tile = side² = ² m² = m² Area of square tiles x Number of tiles = Area of the floor ⇒ Number of tiles = ⇒ Number of tiles = ⇒ Number of tiles = 243 x 16 ⇒ Number of tiles = 3,888 Rate per tile = ₹ 6 per tile Total cost = ₹ 3,888 x 6 = ₹ 23,328 Hence, the number of tiles is 3,888 and the cost of the tiles is ₹ 23,328. (ii) Width of the margin on each side = 1.5 m Length of the inner floor = 18 m \- 1.5 m \- 1.5 m = 18 \- 3 m = 15 m Breadth of the inner floor = 13.5 m \- 1.5 m \- 1.5 m = 13.5 \- 3 m = 10.5 m As we know, the area of the floor = length x breadth = 15 x 10.5 m² = 157.5 m² Side of the square tile = 25 cm = m = m As we know, the area of a tile = side² = ² m² = m² Area of square tiles x Number of tiles = Area of the floor ⇒ Number of tiles = ⇒ Number of tiles = ⇒ Number of tiles = 157.5 x 16 ⇒ Number of tiles = 2,520 Rate of tiles = ₹ 6 per tile Total cost = ₹ 2,520 x 6 = ₹ 15,120 Hence, the number of tiles is 2,520 and the cost of the tiles is ₹ 15,120.

Mathematics

Area Trapezium Polygon

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