What is the minimum number of square tiles required to completely cover a rectangular floor measuring 5.25 m by 5.10 m?

Given:

The dimensions of the rectangular floor are:

Length (l) = 5.25 m

Width (w) = 5.10 m

Formula used:

To find the minimum number of square tiles, we calculate the side of the largest square tile that can exactly divide both the length and width of the floor using the HCF (Highest Common Factor).

Number of tiles = Area of floor / Area of one tile

Area of floor = l × w

Area of one tile = (HCF)²

Calculation:

l = 5.25 m = 525 cm

w = 5.10 m = 510 cm

HCF of 525 and 510:

Prime factorization of 525 = 3 × 5² × 7

Prime factorization of 510 = 2 × 3 × 5 × 17

Common factors = 3 × 5 = 15 ⇒ HCF = 15 cm

Area of floor = 525 × 510 = 267750 cm²

Area of one tile = 15 × 15 = 225 cm²

Number of tiles = 267750 / 225

⇒ Number of tiles = 1190

∴ The correct answer is option (1).