a rectangular courtyard is 57m 50cm long and 22 m board . determine the least possible number of square stones of the same size required to pave it ?
the yard is 5750x2200
GCD(5750,2200) = 50
so, using 50x50 cm stones will use the fewest
Now just figure how many that will be.
what is gcd ?
Largest number of four digit divisible by 18,25 35
5060
To determine the least possible number of square stones required to pave the rectangular courtyard, you need to find the common factor between the length and the width of the courtyard.
First, let's convert the length and width from meters and centimeters to centimeters for uniformity:
Length = 57 m 50 cm = 57 * 100 cm + 50 cm = 5750 cm
Width = 22 m = 22 * 100 cm = 2200 cm
Now, let's calculate the common factor between the length and width by finding the greatest common divisor (GCD) of 5750 and 2200. One way to find the GCD is by using the Euclidean algorithm.
1. Divide 5750 by 2200:
5750 ÷ 2200 = 2 remainder 1350
2. Divide 2200 by 1350:
2200 ÷ 1350 = 1 remainder 850
3. Divide 1350 by 850:
1350 ÷ 850 = 1 remainder 500
4. Divide 850 by 500:
850 ÷ 500 = 1 remainder 350
5. Divide 500 by 350:
500 ÷ 350 = 1 remainder 150
6. Divide 350 by 150:
350 ÷ 150 = 2 remainder 50
7. Divide 150 by 50:
150 ÷ 50 = 3 remainder 0
Since we have a remainder of 0, the last divisor used (50) is the GCD of 5750 and 2200.
Therefore, the least possible size of the square stones would be 50 cm by 50 cm.
To calculate the number of square stones, we divide the area of the courtyard by the area of a single square stone.
The area of the courtyard = Length × Width
= 5750 cm × 2200 cm
= 12,650,000 cm²
The area of a single square stone = Side × Side
= 50 cm × 50 cm
= 2500 cm²
So, the number of square stones required = Area of the courtyard ÷ Area of a single square stone
= 12,650,000 cm² ÷ 2500 cm²
= 5060
Therefore, the least possible number of square stones of the same size required to pave the rectangular courtyard is 5060.