The dimensions of a room are 30 m and 18 m. Find the largest number of square tiles required to cover the floor of the room

Appeared in: DSSSB 6 September 2024

Explanation

The question implicitly asks for the least number of identical square tiles needed, which requires using the largest possible tile size.
The side length of the largest possible square tile is the Highest Common Factor (HCF) of the room's dimensions (30 m and 18 m).
The HCF of 30 and 18 is 6. Therefore, each tile must be 6m x 6m.
The area of the room is 30 m × 18 m = 540 m², and the area of one tile is 6 m × 6 m = 36 m².
The number of tiles required is the total area divided by the tile area: 540 ÷ 36 = 15.

Option A: This result (90) is obtained by incorrectly dividing the room's area (540) by the HCF (6). Area must be divided by area, not by a length.
Option C: This value (30) is the length of the room. It is one of the given parameters of the problem, not the solution.
Option D: A tile of 10m x 10m would not fit perfectly along the 18m side of the room, as 18 is not divisible by 10. Tiles must fit the dimensions exactly without being cut.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of Highest Common Factor (HCF) to find the minimum number of square tiles to cover a rectangular area as background academic context rather than a clinical decision trigger.
While this is a mathematics problem, the underlying principle of optimizing space and resources is highly relevant in healthcare settings.
Tasks such as planning the layout of a ward, an operating room, or a storage area to maximize efficiency and safety involve similar spatial reasoning.
A nurse manager might need to calculate how many patient beds, IV poles, or equipment units can fit into a specific area, requiring an understanding of dimensions and area.

How to Approach the Question

First, analyze the question. Although it asks for the 'largest number' of tiles, the standard interpretation for this problem type is to find the 'least number' of identical square tiles, which requires finding the largest possible tile size.
To find the side length of the largest possible square tile, you must calculate the Highest Common Factor (HCF) of the room's dimensions.
Calculate the HCF of 30 and 18.
Once you have the side length of the tile (the HCF), calculate the area of one tile (side × side).
Calculate the total area of the room (length × width).
Finally, divide the total area of the room by the area of one tile to find the number of tiles required.

Concept Tested & Keywords

Concept Tested: Application of Highest Common Factor (HCF) to find the minimum number of square tiles to cover a rectangular area.
Stem keywords: dimensions, room, 30 m, 18 m, square tiles
Lead-in keywords: Find, largest number

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Practise the full DSSSB 6 September 2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.