Question

A rectangular courtyard a 15 meters and 17 cm long 9 meters and 2 cm 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

Answer 1

Concept

LCM stands for least whole number. the smallest amount integer of two numbers is that the smallest number which may be a multiple of both of them.

Given

There is a rectangular courtyard of length $15$ meters and $17$cm and breadth is $9m \text{ and }2cm$ which is of squared tiles and every one tiles are of the identical size.

Find

We have to seek out the biggest size of the tile.

Solution

The length of the rectangular courtyard is $1500cm+17cm=1517cm$.

The breadth of the rectangular courtyard is $900cm+2cm=902cm$.

Now, we've got to search out H.C.F of  $1517$ and $902$.

$1517=37\times 41$

$902=2\times 11\times 41$

Therefore, common factors are $41.$

Hence largest size of square tiles which will be paved exactly with square tiles is $41cm.$

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Answer 2

There is a rectangular courtyard

Length of rectangular courtyard is

$15m \: and \: 17cm$

let's change this into centimeters

$1m = 100cm \\ 15m = 1500cm$

Now length of the courtyard is

$length = 1500 + 17 \\ = 1517cm$

Given the breadth of the courtyard is

$breadth = 9m \: and \: 2cm$

let's change it into centimeters

$9m = 900cm$

Now breadth of the courtyard is

$breadth = 900 + 2 \\ = 902cm$

We need to arrange square tiles of same size in this rectangular courtyard. Let's find what is the largest size of the tile that could be used for this purpose.

For that we can use the concept of HCF. HCF gives us the highest common factor by which we can get highest size of the tile that could be used in the rectangular courtyard.

Let's find HCF of

$1517 \: and \: 902$

Let's write prime factors for both the numbers

$1517 = 37 \times 41 \\ 902 = 2 \times 11 \times 41$

Common factor of both the numbers is

$41$

Hence HCF of both the numbers is

$41$

Therefore, the largest size of the tile that could be used in the rectangular courtyard is of

$41cm$

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