Select the alternative which represents three out of the five alternative…

When a shape is dissected into pieces by drawing new straight boundary segments inside it, each resulting piece is bounded only by portions of the original outline plus whichever of the new segments enclose it — so a piece's total side-count is fixed by exactly how many boundary segments, original and newly drawn together, run around it. Checking a candidate piece against a dissection is therefore mostly a matter of counting its sides and comparing its proportions to what those specific cuts could actually enclose, then confirming that matching edges are equal in length.

In the given diagram, two new points are marked inside the equilateral triangle's outline: one lies strictly inside the triangle, close under the apex; the other lies on the right-hand edge, partway between the apex and the bottom-right corner. Three straight segments are then drawn: from the bottom-left corner to the interior point, from the interior point to the point on the right edge, and directly from the bottom-left corner to that same point on the right edge. Together these three segments enclose a long, narrow three-sided sliver near the apex. The rest of the triangle, which shares the bottom-left corner with this sliver, is split by it into two further pieces: a four-sided piece bounded by the left edge, the first two new segments, and the upper part of the right edge; and a three-sided piece bounded by the third new segment, the lower part of the right edge, and the full bottom edge.

Figure 5's tall, narrow spike matches the sliver piece near the apex, figure 1's clean three-sided outline matches the bottom-right piece, and figure 3's four-sided outline, with its single inward notch, matches the four-sided piece formed between the first two segments.

• Figure 2's boundary has a zig-zag, double-notch outline; none of the three pieces enclosed by these particular segments has two separate inward notches, so figure 2 does not correspond to any piece of this dissection.

• Figure 4's boundary runs to six straight sides; none of the three pieces enclosed by these particular segments has more than four sides, so figure 4 does not correspond to any piece of this dissection either.

Fitted together edge to edge, figures 1, 3 and 5 reconstruct the equilateral triangle exactly, confirming that 135 is the correct combination.