Question

Find the leash number of square tiles required to pave the ceiling of a room 15 m 17 cm long and 9 m 2 cm broad.

Answer 1

It is given that:
Length of a tile = 15 m 17 cm = 1517 cm [∵ 1 m = 100 cm]
Breadth of a tile = 9 m 2 cm = 902 cm
∴ Side of each square tile = HCF (1517, 902)
Prime factorisation:
1517 = $37\times 41$
902 = $22\times 41$
∴ HCF = Product of smallest power of each common prime factor in the numbers = 41
∴ Required number of tiles = $\frac{\mathrm{Area}\mathrm{of}\mathrm{ceiling}}{\mathrm{Area}\mathrm{of}\mathrm{one}\mathrm{tile}}$ = $\frac{1517\times 902}{41\times 41}$ = $37\times 22$ = 814