📄 Squares cut from a sheet, with a strip left over

A closer look at one question · SMC 2026 mock, Question 26 (bank id C1)

A rectangular sheet of paper was cut into a MAXIMUM of 18 squares of side 4 cm, leaving an L-shaped strip over. The sheet's length is 26 cm. What is the PERIMETER of the sheet before it was cut?

1 Fit the 4 cm squares along the 26 cm length

26 cm
44 44 44 2

26 ÷ 4 = 6 remainder 2 — so 6 squares fit across, and a 2 cm strip of paper is wasted down that side.

2 18 squares, 6 per row — so there are 3 ROWS

4
4
4
4
4
4
2
4
4
4
4
4
4
2
4
4
4
4
4
4
2
1 cm strip along the bottom

18 ÷ 6 = 3 rows, each 4 cm tall, so the squares use 3 × 4 = 12 cm of the sheet's breadth. The leftover strip along the bottom is 1 cm, so the sheet's breadth is 12 + 1 = 13 cm.

3 Perimeter of the WHOLE sheet

2 × (26 + 13) = 2 × 39 = 78 cm.

78 cm

The trap: trying to get the breadth by dividing the squares' AREA (18 × 16 = 288 cm²) by 26. The L-strip is wasted paper, so the squares' area is NOT the paper's area.