Each student desk in a classroom has a rectangular desktop that measures 60 cm by 45cm .Some of these desks are arranged ,side by side .
Find the least length of a side of the square .
AND the number of rows and colums of desk used to form the large square table.
a) 180 cm
b) 3 columns and 4 rows.
Step-by-step explanation:
One side must be multiples of 45 and other side 60 and both sides should be equal.
i.e. 45 columns = 60 Rows
//Find the GCF.
GCF of 45, 60 = 15.
So for 3 columns of one side, you will need have 4 rows of other side to make the lengths equal
the least square of side that can be formed = 45*4 = 60*3 = 180cm
b) the number of rows and columns to form the desk would be 4 rows and 3 columns
To find the least length of a side of the square, we need to find the greatest common divisor (GCD) of the lengths (60 cm and 45 cm) of the rectangular desktops.
Step 1: Find the GCD of 60 cm and 45 cm.
The prime factorization of 60 is 2^2 × 3 × 5, and the prime factorization of 45 is 3^2 × 5.
The common factor between 60 and 45 is 3 × 5 = 15.
Thus, the GCD of 60 cm and 45 cm is 15 cm.
Therefore, the least length of a side of the square is 15 cm.
To find the number of rows and columns of desks used to form the large square table, we need to divide the length and width of the square by the length and width of each desk.
Step 2: Find the number of rows.
Divide the length of the square (15 cm) by the length of each desk (60 cm).
15 cm ÷ 60 cm = 0.25 rows
Since we cannot have fractional rows, we discard the decimal part and consider only the whole number. Therefore, the number of rows is 0.
Step 3: Find the number of columns.
Divide the width of the square (15 cm) by the width of each desk (45 cm).
15 cm ÷ 45 cm = 0.33 columns
Again, since we cannot have fractional columns, we consider only the whole number. Therefore, the number of columns is 0.
Therefore, the large square table cannot be formed using the given rectangular desks, as there are not enough desks to create a square table.
To find the least length of a side of the square formed by arranging the student desks, we need to find the greatest common divisor (GCD) of the length (60 cm) and width (45 cm) of the desktop.
Step 1: Calculate the GCD (Greatest Common Divisor):
To find the GCD of 60 cm and 45 cm, you can use a few different methods, such as prime factorization, the Euclidean algorithm, or a calculator with a GCD function.
Using the Euclidean algorithm, you can start by dividing the larger number (60 cm) by the smaller number (45 cm) and finding the remainder:
60 cm ÷ 45 cm = 1 remainder 15 cm
Then, divide the divisor (45 cm) by the remainder (15 cm) and find the new remainder:
45 cm ÷ 15 cm = 3 remainder 0 cm
Since the remainder is 0, the GCD is the divisor of the last successful division, which is 15 cm.
Therefore, the GCD of 60 cm and 45 cm is 15 cm.
Step 2: Determine the least length of a side of the square:
Since the square should have equal sides, the least length of a side of the square would be equal to the GCD.
Thus, the least length of a side of the square would be 15 cm.
Step 3: Calculate the number of rows and columns of desks used to form the large square table:
To calculate the number of rows and columns, divide the length and width of the square table (both equal to the least length of a side of the square) by the dimensions of a single desk.
Number of rows: 15 cm ÷ 45 cm = 1
Number of columns: 15 cm ÷ 60 cm = 0.25
Since you can't have a fractional number of columns (as each desk is a whole unit), you can round up to the nearest whole number. So, the number of columns would be 1.
Therefore, the square table is formed by arranging the desks in 1 row and 1 column.