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. What is the largest size of the tile which could be used for the purpose?
A. \[14cm\]
B. \[21cm\]
C. \[42cm\]
D. None of these

Answer 1

Hint: As we know rectangle is a two-dimensional shape having four sides and four corners and as mentioned the courtyard is rectangular and to find the size of the tile, calculate length and breadth of the rectangular courtyard. Then find out the HCF of both the terms and after calculating find out the common factor obtained in the HCF of length and breadth.

Complete step by step answer:
Let us calculate the Length of the rectangular courtyard, as given the courtyard is $5.25$ metres wide, hence the Length of the rectangular courtyard is
\[5.25m = 525cm\]
Length=\[525cm\]
Next let us calculate the Breadth of the rectangular courtyard, as given the courtyard is $3.78$ metres wide, hence the Breadth of the rectangular courtyard is
\[3.78m = 378cm\]
Breadth=\[378cm\]
Therefore, Length of the rectangular courtyard is \[525cm\] and Breadth of the rectangular courtyard is \[378cm\].
Now let us find the H.C.F of length and breadth
\[525 = 5 \times 5 \times 3 \times 7\]
\[378 = 2 \times 3 \times 3 \times 3 \times 7\]
The common factors are \[3 \times 7\].
Therefore H.C.F is $21$cm.
Hence, the largest size of square tiles that can be paved exactly with the square tiles is $21$cm.

Therefore, option \[B\] is the right answer.

Note:
As rectangle consists of four sides and to calculate the largest size of tiles in rectangular courtyard is measuring the length and breadth then find out the H.C.F of both the terms and find out the product of the common factor as the size of tile is calculated by length \[ \times \] breadth of the tile.