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
Clearly, a 50cm square stone is the largest that will evenly tile both dimensions.
So, how many of those will fit in each direction?
50 cm
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
To determine the least number of square stones required to pave the rectangular courtyard, we need to find the area of the courtyard and the area of each square stone.
Step 1: Convert the measurements to the same unit.
The length of the courtyard is 57m 50cm, which is equivalent to 57.50m.
The breadth of the courtyard is 22m.
Step 2: Calculate the area of the courtyard.
Area of a rectangle = length × breadth
Area = 57.50m × 22m
Area = 1265 square meters
Step 3: Determine the area of each square stone.
Since all the square stones are of the same size, we need to find the area of one square stone. To do that, we need to know the side length of the square stone.
Step 4: Choose a side length for the square stone.
Let's assume the side length of each square stone is 'x'.
Step 5: Calculate the area of one square stone.
Area of a square = side length × side length
Area = x× x
Area = x^2
Step 6: Determine the least number of square stones required.
To find the least number of square stones, we need to divide the area of the courtyard by the area of one square stone.
Number of square stones = Area of courtyard / Area of one square stone
Number of square stones = 1265 square meters / x^2
At this point, we need the value of 'x' (the side length of each square stone) to calculate the least number of square stones.