A rectangular courtyard is 57m 50 cm long and 22m broad. Determine the least possible number of square stones of the same size required to pave it
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To determine the least possible number of square stones required to pave the rectangular courtyard, we need to find the common factor of the length and breadth of the courtyard.
First, let's convert the length and breadth to the same units. Since we have 1 meter equal to 100 centimeters, the length of the courtyard is 57 meters and 50 centimeters, which is equal to 5750 centimeters. Similarly, the breadth is 22 meters, which is equal to 2200 centimeters.
Now, let's find the greatest common divisor (GCD) of 5750 and 2200 to determine the common factor. One way to find the GCD is to use the Euclidean algorithm:
1. Divide the larger number (5750) by the smaller number (2200): 5750 ÷ 2200 = 2 with a remainder of 1350.
2. Now, divide the smaller number (2200) by the remainder (1350): 2200 ÷ 1350 = 1 with a remainder of 850.
3. Repeat the previous step: 1350 ÷ 850 = 1 with a remainder of 500.
4. Continue: 850 ÷ 500 = 1 with a remainder of 350.
5. Lastly: 500 ÷ 350 = 1 with a remainder of 150.
The final non-zero remainder (150) is the greatest common divisor (GCD) of 5750 and 2200.
Therefore, the common factor of the length and breadth of the courtyard is 150 centimeters. It means that the square stones should have sides of 150 centimeters.
To determine the number of square stones required, we can divide the length and breadth of the courtyard by the length of one square stone:
Number of stones in length = Length of courtyard ÷ Length of one stone
= 5750 cm ÷ 150 cm
= 38.33
Since we can't have a partial stone, we need to consider the next whole number. Therefore, the number of stones in length is 39.
Similarly, we calculate the number of stones in breadth:
Number of stones in breadth = Breadth of courtyard ÷ Length of one stone
= 2200 cm ÷ 150 cm
= 14.67
Rounded up to the next whole number, the number of stones in breadth is 15.
Finally, to calculate the total number of stones required, we multiply the number of stones in length by the number of stones in breadth:
Total number of stones = Number of stones in length × Number of stones in breadth
= 39 × 15
= 585
Therefore, the least possible number of square stones required to pave the rectangular courtyard is 585.