▭ Two rectangles overlapping to make a square

A closer look at one question · SMC 2026 mock, Question 28 (bank id C3)

Two IDENTICAL rectangles overlap, and the overlap is Square A. Square A's area is 9 cm², and each rectangle's area is 50 cm², with length = 2 × breadth. Find the perimeter of the whole figure (not drawn to scale).

1 See the overlap

A

2 Square A's side, then the rectangle's sides

Area of A = 9 cm², so its side is 3 cm (since 3 × 3 = 9).

Each rectangle has area 50 cm² and length = 2 × breadth, so breadth × 2 × breadth = 50 → breadth × breadth = 25 → breadth = 5 cm, and length = 10 cm.

3 Add both rectangles' perimeters, then remove the HIDDEN edges

1 rectangle
2 × (10 + 5) = 30 cm

Two rectangles separately would total 2 × 30 = 60 cm — but where they overlap, TWO sides of Square A are hidden inside EACH rectangle: that is four 3 cm edges in all.

Figure
60 − (4 × 3) = 48 cm
48 cm

The trap: taking Square A's side as 9 cm instead of 3 cm (9 is the AREA), or answering 60 by forgetting that the overlap hides edges.