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.

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Solution

The correct option is B 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
$378 = 2 \times 3 \times 3 \times 3 \times 7$
$525 = 3 \times 5 \times 5 \times 7$
$\Rightarrow H C F o f 378 a n d 525 = 3 \times 7 = 21$
$∴ L o n g e s t s i d e o f t h e t i l e = 21 c m$
$\Rightarrow n \times 3 = 21 = 7 \times 3$
$\Rightarrow n = 7$

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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 × 3) cm. Find n.

The correct option is B 7Given: 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=2×3×3×3×7 525=3×5×5×7 ⇒HCF of 378 and 525=3×7=21 ∴Longest side of the tile=21 cm ⇒n×3=21=7×3 ⇒n=7

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.