Select the alternative which represents three out of the five alternative…
2025
Select the alternative which represents three out of the five alternative figures which when fitted into each other would form an equilateral triangle.
Answer: C. 345 — In this type of figure-reconstruction question, three of the five given fragments must fit together — some edges glued flush against a matching edge on…
- A.
234
- B.
134
- C.
345
- D.
245
Attempted by 11 students.
Show answer & explanation
Correct answer: C
In this type of figure-reconstruction question, three of the five given fragments must fit together — some edges glued flush against a matching edge on another fragment (an interior seam), the rest left exposed to form the boundary — so that the exposed edges trace out one target shape with no gap or overlap. Here the target is an equilateral triangle: three equal sides, three 60° corners. To find the right trio, measure each fragment's edges: whichever two fragments share an edge of the same length can be joined along it (as an interior seam or as two collinear pieces of one side), while the fragment's remaining edges must then close up the rest of the boundary at the correct angles.
Checking the five given fragments against this rule:
Figure | Shape | Key feature | Role in the triangle |
|---|---|---|---|
(1) | Right-angled triangle | One corner is 90°; no edge matches figures 3/4/5 | Not used — a 90° corner cannot form one of the triangle's 60° corners |
(2) | Trapezoid (4 sides) | No edge matches figures 3/4/5 | Not used — its edges do not line up with figures 3, 4 and 5 |
(3) | Scalene triangle | Longest edge is the same length as figure (5)'s long edge | Used — contributes one full side |
(4) | Narrow triangular sliver | Its two shorter edges match the leftover edges of (3) and (5) | Used — fills the gap between (3) and (5), completing the third side and corner |
(5) | Four-sided fragment | Long diagonal edge is the same length as figure (3)'s long edge | Used — contributes the second full side |
Figure (3)'s longest edge and figure (5)'s longest (diagonal) edge are the same length, so each can stand as one full side of the triangle. Figure (4) is the smallest fragment; its two shorter edges match the remaining (shorter) edges left on figures (3) and (5), so it slots into the gap between them, closing the third side and the corner between it — with no leftover gap and no overlap.
So figures (3), (4) and (5) are the three fragments that fit together to form the equilateral triangle.