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A rectangular courtyard 140cm long 525cm 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)64cm
- b)35cm
- c)21cm
- d)28cm
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A rectangular courtyard 140cm long 525cm wide is to be paved exactly w...
30 cm = 4 x 5 x 7
525 cm = 5 x 5 x 3 x 7
Hence common factors are 5 and 7
Hence LCM = 5 x 7 = 35
Most Upvoted Answer
A rectangular courtyard 140cm long 525cm wide is to be paved exactly w...
Problem: To find the largest size of a square tile that can be used to completely pave a rectangular courtyard.
Given: Length of courtyard = 140cm, width of courtyard = 525cm.
Solution:
To find the largest size of the tile, we need to find the common factor of both the length and width of the courtyard.
Step 1: Find the HCF (Highest Common Factor) of 140 and 525.
We can use the prime factorization method to find the HCF.
140 = 2 × 2 × 5 × 7
525 = 3 × 5 × 5 × 7
Multiplying the common factors, we get:
HCF = 5 × 7 = 35
Step 2: The largest size of the tile that can be used is equal to the HCF.
Therefore, the largest size of the tile that can be used is 35cm.
Hence, option (B) is the correct answer.
Note: It is important to find the HCF of the length and width of the courtyard to ensure that the entire area is covered without leaving any gaps. Using a tile size that is not a factor of both the length and width will result in incomplete paving.
Given: Length of courtyard = 140cm, width of courtyard = 525cm.
Solution:
To find the largest size of the tile, we need to find the common factor of both the length and width of the courtyard.
Step 1: Find the HCF (Highest Common Factor) of 140 and 525.
We can use the prime factorization method to find the HCF.
140 = 2 × 2 × 5 × 7
525 = 3 × 5 × 5 × 7
Multiplying the common factors, we get:
HCF = 5 × 7 = 35
Step 2: The largest size of the tile that can be used is equal to the HCF.
Therefore, the largest size of the tile that can be used is 35cm.
Hence, option (B) is the correct answer.
Note: It is important to find the HCF of the length and width of the courtyard to ensure that the entire area is covered without leaving any gaps. Using a tile size that is not a factor of both the length and width will result in incomplete paving.
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