Question

(1) A rectangular courtyard with length 7 m 20 cm and breadth 3 m 60 cm is to be paved with square stones of the same size. Find the least number of such stones required.

Answer 1

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$\huge{ \sf{ \underline{ \purple{Answer...}}}}$

♠️ GiveN:

• Length of courtyard = 7 m 20 cm
• Breadth of courtyard = 3 m 60 cm
• This courtyard is to be paved with square stones

♠️To FinD:

• Least number of square stones required...?

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$\huge{ \underline{ \rm{ \purple{Explanation...}}}}$

In the question, it is given that the tiles are squares, so the sides are equal. It means the sides of courtyard is divisible by the side of square stones. For the minimum no. of stones, the side of the square need to the highest common factor (HCF) of sides of courtyard.

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So, we need to find the HCF of 7 m 20 cm and 3 m 60 cm, this will be the side of the square. Then, we will find the area of each square stone and divide it by the area of courtyard to find the no. of tiles.

♦️ In this way, we will solve this question

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$\huge{ \underline{ \sf{ \purple{ Solution...}}}}$

First of all, we need to convert the sides into cm, for easy calculation or to make it easier to find HCF,

We know, 1 m = 100 cm

Length of the courtyard = 7 m 20 cm = 720 cm

Breadth of the courtyard= 3 m 60 cm = 360 cm

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♠️ The edge must be the common factor of the sides of the courtyard i.e. Minimum no. of stones = HCF of 720 cm and 360 cm.

Finding HCF of 720 and 360, by prime factorization

$\large{ \sf{\rightarrow \: 720 = 2 \times \red{ \underline{2 \times 2 \times 2 \times 3 \times 3 \times 5}}}} \\ \\ \large{\sf{\rightarrow \: 360 = \red{ \underline{2 \times 2 \times 2 \times 3 \times 3 \times 5}}}} \\ \\ \large{\sf{ \therefore{hcf \: of \: 720 \: and \: 360 = 360}}}$

So, Maximum side of square tile = 360 cm

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For finding the no. of square tiles ,we need to divide the area of the courtyard by area of courtyard

Finding the no. of required tiles,

$\large{\sf{ \star{ \: required \: no. \: of \: tiles = \frac{area \: of \: courtyard}{area \: of \: square \: stones} }}} \\ \\ \large{\boxed{ \green{\sf{ \ast \: area \: of \: square = side \times side}}}} \\ \\ \large{\sf{ \rightarrow \: required \: no. \: of \: stones = \cancel{ \frac{720 \times 360}{360 \times 360}}}} \\ \\ \large{\sf{ \rightarrow \: required \: no. \: of \: stones= \boxed{ \red{2}}}}$

✍Thus, the least no. of square stones = 2

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