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 a complete square.

  1. A.

    145

  2. B.

    234

  3. C.

    245

  4. D.

    135

Attempted by 2 students.

Show answer & explanation

Correct answer: D

Concept: When a closed figure such as a square is cut along internal lines into several pieces, each resulting piece is a smaller polygon with fixed sides and angles taken from the whole boundary. To find which three of five candidate figures reassemble the square, trace the internal cut lines, note the shape of each region produced (number of sides, right angles, notches), and match each region — allowing rotation but not mirroring — to one candidate figure of the same shape.

Application: The square in the solution figure is cut by lines running from a point on its left edge, producing three regions:

  1. A triangular region bounded by the top edge, the left edge, and a diagonal to the top-right corner — a right-angled triangle, matching piece (1).

  2. A five-sided (pentagon) region in the middle, bounded by the zig-zag cut lines — matching piece (3).

  3. The remaining region at the bottom-right, whose boundary has a notch that interlocks exactly with the pentagon's edge — matching the concave, arrow-shaped piece (5).

Cross-check: Checking the other pieces confirms none of them can replace these three:

  • Piece (2) has an extra right-angle step partway along one side that no region of the cut square produces, so it cannot replace piece (1).

  • Piece (4) is a kite-shaped quadrilateral whose notch and angles do not match the sharply-notched middle region, so it cannot replace piece (3).

  • Fitting pieces (1), (3) and (5) together (rotating as needed, never flipping) exactly reconstructs the square with no gap or overlap: piece (1)'s vertical and horizontal edges align with the square's left and top edges, and piece (5)'s notch fits into the complementary cut on piece (3)'s boundary.

Result: Hence pieces 1, 3 and 5 combine to form the complete square — option 135.

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