A courtyard is in the shape of a rectangle of length 11.2 and 7.2 breadth.find the measure of the largest square shaped tile that can be used (in the whole),to cover the courtyard completely ..how many tiles are needed for purpose.
the tile has to be evenly divisible into 11.2 and 7.2
area=11.2*7.2=80.64
I see that .2 will go in both evenly.
tiles .2x.2= .04 area
number tiles=80.64/.04
Mad
To find the measure of the largest square-shaped tile that can be used to cover the courtyard completely, we need to determine the greatest common divisor (GCD) of the length and breadth of the courtyard.
The GCD will represent the length of each side of the largest square tile that can be used. The formula to find the GCD is:
GCD = gcd(length, breadth)
In this case, the length of the courtyard is 11.2 and the breadth is 7.2.
To calculate GCD, we can use the Euclidean algorithm.
1. Start by dividing the larger number (11.2) by the smaller number (7.2).
11.2 ÷ 7.2 = 1, remainder 4.0
2. Next, divide the smaller number (7.2) by the remainder obtained (4.0).
7.2 ÷ 4.0 = 1, remainder 3.2
3. Continue dividing the previous remainder (4.0) by the new remainder (3.2).
4.0 ÷ 3.2 = 1, remainder 0.8
4. Now, divide the new remainder (3.2) by the last obtained remainder (0.8).
3.2 ÷ 0.8 = 4, remainder 0
5. When the remainder becomes 0, the last obtained divisor (0.8) is the GCD.
Therefore, the GCD of 11.2 and 7.2 is 0.8.
The measure of the largest square-shaped tile that can be used to cover the courtyard completely is 0.8 units.
To determine the number of tiles needed to cover the courtyard completely, divide the length and breadth of the courtyard by the side length of the square tile:
Number of tiles = (length ÷ GCD) × (breadth ÷ GCD)
Number of tiles = (11.2 ÷ 0.8) × (7.2 ÷ 0.8)
Number of tiles = 14 × 9
Number of tiles = 126
Therefore, a total of 126 square-shaped tiles are needed to cover the courtyard completely.
Area of a rectangle=l*b.
11.2*7.2=80.64
Number of tiles=80.64÷04