A floor is 12 m by 9 m. If tiles of 1.5 m × 1.5 m are used, how many tiles are needed?

Correct — A. Count the tiles along each side, then multiply.

Along 12 m: 12 ÷ 1.5 = 8 tiles
Along 9 m: 9 ÷ 1.5 = 6 tiles
Multiply: 8 × 6 = 48 tiles

Check by area: 108 m² ÷ 2.25 m² = 48 → option (a)

Why the others are wrong

• (b)
  68 — 68 tiles would cover 68 × 2.25 = 153 m², far more than the 108 m² floor.
• (c)
  72 — 72 is 108 ÷ 1.5, the floor area divided by the tile's side instead of its area. One tile covers 1.5 × 1.5 = 2.25 m².
• (d)
  80 — 80 tiles would cover 80 × 2.25 = 180 m², two-thirds more than the 108 m² floor.

Tiling a rectangle: number of tiles = floor area ÷ tile area, when the tiles fit without cutting.

Here they fit exactly. 1.5 m goes into 12 m 8 times and into 9 m 6 times, so 48 whole tiles cover the floor with nothing left over.

Counting along each side first is the safer habit. A whole-number area ratio can hide a misfit: a 4 m × 9 m floor with 3 m tiles gives 36 ÷ 9 = 4, yet 3 does not go into 4.

Key facts

• Number of tiles = floor area ÷ tile area, when the tiles fit exactly.
• A 1.5 m × 1.5 m tile covers 2.25 m².
• 12 × 9 = 108 m², and 108 ÷ 2.25 = 48.

Common traps

• Dividing the floor area by the tile's side, 108 ÷ 1.5 = 72, instead of by its area.
• Squaring 1.5 as 2.5 instead of 2.25. That gives 43.2 tiles, and a non-whole count is a sign of a slip.

No directly related past PYQ was found.