Select the alternative which represents three out of the five alternative…
2023
Select the alternative which represents three out of the five alternative figures which when fitted into each other would form equilateral triangle.

- A.
135
- B.
124
- C.
245
- D.
345
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept: In a figure-formation ("grouping and assembling") puzzle, a target shape can be rebuilt only from pieces whose cut edges pair up exactly — every concave notch on one piece must key into a matching convex point on another, and the outer edges of the chosen pieces, laid together, must trace the full outline of the target shape with no gap and no overlap.
Application: Here the five pieces have very different profiles:
Figure (1) is a plain wedge with a single straight cut and no internal notch.
Figures (2) and (4) each have one internal notch sitting above a wide base — both are shaped to sit at the bottom of the triangle.
Figure (3) is a dart with one notch and a point that projects up and to one side.
Figure (5) is a small piece with one shallow notch, sized to fill a narrow corner.
Figures (3), (4) and (5) key into each other directly: figure (4) supplies the broad notched base, figure (3)'s projecting point sits exactly into that notch to build the triangle's midsection, and figure (5)'s small notch closes the narrow gap left near the apex. Their outer edges then trace one unbroken equilateral triangle, exactly as shown below.

Cross-check: figure (4) is the only piece with a notch sitting above a wide base, figure (3) is the only piece whose dart shape gives it both a notch and a genuine projecting point, and figure (5) is the only small piece with a shallow notch of its own — no shape repeats among the three, and every notch in the group is met by a matching projecting point, so the assembled boundary traces one unbroken equilateral triangle, matching the areas shown above (two comparable-sized regions plus one visibly smaller region).
So the equilateral triangle is formed by figures (3), (4) and (5).