Question

A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad. It is to be paved with
square tiles of the same size. Find the least possible number of such tiles.-
​

Answer 1

Answer:

length =1872cm

width=1320cm

square tile must be the common divisor of the courtyard

max edge of tile=hcf of 1872&1320 =24

So, no of tiles=area of couryard/

Area of square tile =1870×1320/(24)(24)=4290

Answer 2

Answer:

Step-by-step explanation:

Given :-

Length of courtyard = 18 m  72 cm = 1872 cm

Breadth of courtyard = 13 m 20 cm = 1320 cm

To Find :-

The least possible number of tiles.

Formula to be used :-

Number of tiles = Area of courtyard/Area of side of tile.

Solution :-

Taking out HCF of 1872 and 1320 using Euclid's Lemma,we get

⇒ 1872 = 1320 × 1 + 552

⇒  1320 = 552 × 2 + 216

⇒  552 = 216 × 2 + 120

⇒  216 = 120 × 1 + 96

⇒  120 = 96 × 1 +24

⇒  96 = 24 × 4 + 0

HCF of 1872 and 1320 = 24

Number of tiles = Area of courtyard/Area of side of tile.

Number of tiles = 1872 × 1320 /24 × 24

Number of tiles = 4290

Hence, the least possible number of such tiles are 4290.