Question

The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Hint:

Whenever a problem asks for "maximum size" or "largest possible" pieces to be cut or fitted without remainder, it is a hint to calculate the H.C.F.

Answer 1

The window dimensions are:
156 cm × 216 cm

Arjun wants to form complete squares of maximum possible size.
This means we must find the side length = HCF (or GCD) of 156 and 216.

Step 1: Find HCF of 156 and 216
216 − 156 = 60
156 − 2×60 = 36
60 − 36 = 24
36 − 24 = 12
24 − 2×12 = 0

So HCF = 12 cm.

Therefore, the maximum size of each square = 12 cm × 12 cm.

Step 2: Find number of such squares
Along length (216 cm): 216 ÷ 12 = 18 squares

Along width (156 cm): 156 ÷ 12 = 13 squares

Total number of squares:
18 × 13 = 234

Final Answers:
Side of each square = 12 cm
Number of squares = 234