Rectangular courtyard is 57m 50cm and 22m broad. Determine the least possible number of square stones of the same size required to pave it.
Length=5750 cm
Width= 2200cm
AREA = length of largest tile=H.C.F of (5750cm and 2200cm)
=2x5x5x4=200cm
Required number of tiles= Area of floor/Area of tile
=5750x2200 / 200x200
=316.25
so, 316.25 is the least possible number of square stone s of the same size to pave it.
math question
Good
To find the largest number that is divisible by 18, 25, and 35, we need to find the least common multiple (LCM) of these three numbers.
The LCM of 18, 25, and 35 is the smallest multiple that is divisible by all three numbers. To find the LCM, we can prime factorize each number and take the highest power of each prime factor.
Prime factorization of 18 = 2 * 3^2
Prime factorization of 25 = 5^2
Prime factorization of 35 = 5 * 7
Taking the highest power of each prime factor, we have:
2^1 * 3^2 * 5^2 * 7^1 = 2 * 9 * 25 * 7 = 3150
So, the largest four-digit number divisible by 18, 25, and 35 is 3150.
To determine the least possible number of square stones required to pave the rectangular courtyard, we need to find the total area of the courtyard and divide it by the area of each square stone.
First, let's convert the dimensions of the courtyard into a consistent unit.
The width of the courtyard is given as 57m 50cm, which we can convert to meters by dividing by 100:
57m 50cm = 57.50m
The breadth of the courtyard is given as 22m.
Next, we calculate the area of the courtyard:
Area = Length x Breadth
Area = 57.50m x 22m
Area = 1265m²
Now, let's assume that each square stone has an area of 1m².
To find the least possible number of square stones required to pave the courtyard, we divide the total area of the courtyard by the area of each square stone:
Number of square stones = Area of courtyard ÷ Area of each square stone
Number of square stones = 1265m² ÷ 1m²
Number of square stones = 1265
Therefore, the least possible number of square stones required to pave the rectangular courtyard is 1265 stones.