Question

A hall-room 39 m 10 cm long and 35 m 70 cm broad is to be covered with equal square tiles. Find the largest tile so that the tiles exactly fit and also find no. of tiles required.

Answer 1

A hall-room 39 m 10 cm long and 35 m 70 cm broad is to be covered with equal square tiles. Find the largest tile so that the tiles exactly fit and also find no. of tiles required.

**Solution:**

Length of the room:

39 m 10 cm = 39 · 100 + 10 = 3910 cm

Width of the room:

35 m 70 cm = 35 · 100 + 70 = 3570 cm

Now we can factor the distances (length and width):

3910 = 2 · 5 · 17 · 23

3570 = 2 · 3 · 5 · 7 · 17

GCF of the length and width is:

GCF(3910, 3570) = 2 · 5 · 17 = 170 cm

Hence, the side of the tile is equal to 170 cm, so the area of one tile is

$$S_{\text{tile}} = (170\,\text{cm})^2 = 28900\,\text{cm}^2.$$

The area of the room:

$$S_{\text{room}} = 3910 \cdot 3570 = 13958700\,\text{cm}^2$$

Number of tiles:

$$\mathrm{N} = \frac{S_{\text{room}}}{S_{\text{tile}}} = \frac{13958700}{28900} = 483 \text{ tiles}$$

**Answer:** side of the tile is 170 cm, number of tiles: 483.