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A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?
- a)160
- b)450
- c)250
- d)325
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved ex...
378 = 2 * 3 * 3 * 3 * 7
525 = 3 * 5 * 5 * 7
Highest Common Factor(HCF) = 3 * 7 = 21
Size of largest tile = 0.21 m by 0.21 m
Minimum Number of tiles = (3.78 * 5.25) / (0.21 * 0.21) = 450
525 = 3 * 5 * 5 * 7
Highest Common Factor(HCF) = 3 * 7 = 21
Size of largest tile = 0.21 m by 0.21 m
Minimum Number of tiles = (3.78 * 5.25) / (0.21 * 0.21) = 450
Most Upvoted Answer
A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved ex...
Number of tiles =n
side length of tile=a
area of n tiles =n×a^2
but area of n tiles =area of rectangle of (l,b)=(3.78,5.25)
~~~n×a^2=3.78×5.25
~~~n×a^2=450×21×21×10^(-4)
~~~n×a^2=450×(21×10^(-2))^2
-: n=450
number of tiles=450
side length of tile=a
area of n tiles =n×a^2
but area of n tiles =area of rectangle of (l,b)=(3.78,5.25)
~~~n×a^2=3.78×5.25
~~~n×a^2=450×21×21×10^(-4)
~~~n×a^2=450×(21×10^(-2))^2
-: n=450
number of tiles=450
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Community Answer
A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved ex...
Calculation of Number of Tiles Required
To find the minimum number of square tiles required to pave the rectangular courtyard, we need to divide the area of the courtyard by the area of each tile.
Area of Courtyard:
Length = 3.78 m
Breadth = 5.25 m
Area = Length x Breadth = 3.78 m x 5.25 m = 19.845 m²
Area of Each Tile:
Let the side of each square tile be 'x' meters.
Area of each tile = x x x = x²
Number of Tiles Required:
Number of tiles = Area of Courtyard / Area of Each Tile
Number of tiles = 19.845 m² / x²
Finding the Minimum Number of Tiles:
To minimize the number of tiles, we need to find the largest square tile that can fit into the courtyard without leaving any gaps.
Since the tiles need to cover the entire courtyard without cutting or overlapping, the side of each tile should be a common factor of both the length and breadth of the courtyard.
Calculating the Common Factor:
Finding the greatest common divisor (GCD) of the length and breadth of the courtyard:
GCD(3.78, 5.25) = 0.15
Number of Tiles with Side x = 0.15:
Number of tiles = 19.845 m² / (0.15 m x 0.15 m) = 450 tiles
Therefore, the minimum number of square tiles required to pave the rectangular courtyard is 450. This corresponds to option (b) in the given choices.
To find the minimum number of square tiles required to pave the rectangular courtyard, we need to divide the area of the courtyard by the area of each tile.
Area of Courtyard:
Length = 3.78 m
Breadth = 5.25 m
Area = Length x Breadth = 3.78 m x 5.25 m = 19.845 m²
Area of Each Tile:
Let the side of each square tile be 'x' meters.
Area of each tile = x x x = x²
Number of Tiles Required:
Number of tiles = Area of Courtyard / Area of Each Tile
Number of tiles = 19.845 m² / x²
Finding the Minimum Number of Tiles:
To minimize the number of tiles, we need to find the largest square tile that can fit into the courtyard without leaving any gaps.
Since the tiles need to cover the entire courtyard without cutting or overlapping, the side of each tile should be a common factor of both the length and breadth of the courtyard.
Calculating the Common Factor:
Finding the greatest common divisor (GCD) of the length and breadth of the courtyard:
GCD(3.78, 5.25) = 0.15
Number of Tiles with Side x = 0.15:
Number of tiles = 19.845 m² / (0.15 m x 0.15 m) = 450 tiles
Therefore, the minimum number of square tiles required to pave the rectangular courtyard is 450. This corresponds to option (b) in the given choices.
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A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?a)160b)450c)250d)325e)None of the AboveCorrect answer is option 'B'. Can you explain this answer?
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A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?a)160b)450c)250d)325e)None of the AboveCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?a)160b)450c)250d)325e)None of the AboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?a)160b)450c)250d)325e)None of the AboveCorrect answer is option 'B'. Can you explain this answer?.
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