Question

a rectangular floor is 2016 cm long and 1560 cm broad.It is to be paved with square tiles of the same size.Find the least possible number of tiles

Answer 1

length of rectangle = 2016 cm
breadth = 1560 cm
HCF of 2016 and 1560 would give the side of a tile⇒ 24
area of one square tile = 24² = 576
area of the rectangle = 2016 * 1560 = 3144960
∴ no. of tiles that can be paved = 3144960 /  576 =5460


Hope it helps..:)

Answer 2

Answer:

The least possible number of tiles required is 5460.

Step-by-step explanation:

Consider the provided information.

The length and breadth of the rectangular floor is 2016 cm and 1560 cm respectively.

In order to find the least possible number of tiles simply find the highest common factor of 2016 and 1560.

2016 = 2×2×2×2×2×3×3×7

1560 = 2×2×2×5×3×13

Therefore, the HCF = 2×2×2×3 = 24

Thus, the side of tile should be 24 cm.

Now, calculate the area of square tile by using the formula:

Area of square = (side)²

Now, replace "side" by 24 cm in the above formula.

Area of tile = (24cm)² = 576 cm²

Now find the area of rectangular floor by using the formula:

Area of rectangle = Length × Width

                             = 2016 cm × 1560 cm

                             = 3144960 cm²

Now divide the area of rectangle with the area of tile which will gives us the number of tiles required.

Number of tiles = $\frac{3144960}{576}$

Number of tiles = 5460

Hence, the least possible number of tiles required is 5460.