Question

A rectangular courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size. The longest side of the tile which could be used for the purpose is (n $\times$ 3) cm. Find n.

• A. 6
• B. 8
• C. 9
• D. 7

Answer 1

The correct option is D 7

Given:
Length of the courtyard = 3.78 m = 378 cm
Width of the courtyard = 5.25 m = 525 cm

Longest sideof the tile = H.C.F. of 378 cm and 525 cm
$378=2\times 3\times 3\times 3\times 7$
$525=3\times 5\times 5\times 7$
$\Rightarrow HCFof378and525=3\times 7=21$
$\therefore Longestsideofthetile=21cm$
$\Rightarrow n\times 3=21=7\times 3$
$\Rightarrow n=7$