A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad. It is

1.	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» Length of the courtyard = 18 m 72 cm = [18(100) + 72] cm [As, 1 m = 100 cm] = 1872 cm The breadth of the courtyard = 13 m 20 cm = [13(100) + 20] cm = 1320 cm To find the maximum edge of the tile we need to calculate HCF of length and breadth, Using Euler’s division lemma: a = pq + r where 0 ≤ r ≤ p 1872 = 1320 × 1 + 552 As 'r' is not equals to 0, So apply Euler's division on 1320 and 552, 1320 = 552 × 2 + 216 As 'r' is not equals to 0, So apply Euler's division on 552 and 216, 552 = 216 × 2 + 120 As 'r' is not equals to 0, So apply Euler's division on 216 and 120, 216 = 120×1 + 96 As 'r' is not equals to 0, So apply Euler's division on 120 and 96, 120 = 96 ×1 + 24 As 'r' is not equals to 0, So apply Euler's division on 96 and 24, 96 = 24 × 4 + 0 Therefore HCF of 1872 and 1320 is 24 Maximum edge can be 24 cm. Number of tile = \(\frac{Area\,of\,courtyard}{Area\,of\,one\,\,tile}\) = \(\frac{1872\times1320}{24\times 24}\) = 4290 tiles

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»

Length of the courtyard = 18 m 72 cm = [18(100) + 72] cm [As, 1 m = 100 cm] = 1872 cm

The breadth of the courtyard = 13 m 20 cm = [13(100) + 20] cm = 1320 cm

To find the maximum edge of the tile we need to calculate HCF of length and breadth,

Using Euler’s division lemma:

a = pq + r where 0 ≤ r ≤ p

1872 = 1320 × 1 + 552

As 'r' is not equals to 0,

So apply Euler's division on 1320 and 552,

1320 = 552 × 2 + 216

As 'r' is not equals to 0,

So apply Euler's division on 552 and 216,

552 = 216 × 2 + 120

As 'r' is not equals to 0,

So apply Euler's division on 216 and 120,

216 = 120×1 + 96

As 'r' is not equals to 0,

So apply Euler's division on 120 and 96,

120 = 96 ×1 + 24

As 'r' is not equals to 0,

So apply Euler's division on 96 and 24,

96 = 24 × 4 + 0

Therefore HCF of 1872 and 1320 is 24

Maximum edge can be 24 cm.

Number of tile = \(\frac{Area\,of\,courtyard}{Area\,of\,one\,\,tile}\) = \(\frac{1872\times1320}{24\times 24}\) = 4290 tiles