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.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Suggest Corrections

Similar questions

Q. 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.

Q. 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. What is the largest size of the tile which could be used for the purpose?

A rectangle courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size what is the largest size of the tile which could be used for the ppurpose ?

Q. A 5.25 m by 3.78 m rectangular courtyard is to be paved with square tiles of the same size such that only tiles are used. What is the largest possible size of such a tile? Also find the number of tiles required.

Q. A rectangular courtyard 378 cm long and 525 cm broad is to be paved exactly with square tiles, all of the same size. The minimum number of such tiles is :

Join BYJU'S Learning Program

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.