Q) The dimensions of a window are 156 cm x 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.

(Q 27 – 30/5/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s understand the question first and approach to solve:

∵ All squares will have both sides of equal size

∴ this side length will be common factor to both sides of window

∵ Sqaure should be of maximum size, hence this square side has to be highest

∴ this square side will be highest factor

∴ we need to calculate the square side length as highest common factor fo both window sides

Step 2: By prime factorisation:

156 = 2 x 2 x 3 x 13

216 = 2 x 2 x 2 x 3 x 3 x 3

∴ HCF of 156, 216 = 2 x 2 x 3 = 12

Therefore, the side length of the square is 12 cm.

Step 3: At window side of 156 cm, squares count will be = = 13

At window side of 216 cm, squares count will be = = 18

∴ Possible number of squares will be 13 x 18 = 234

Therefore, 234 squares will be formed.

Please press “Heart” if you liked the solution.