Question

Shown below is an empty triangle which is to be filled using five tiles. Which option(s) will exactly fill this triangle when all tiles are used? Scaling, Repeating, and Flipping of tiles is not allowed; while rotation is allowed. 

• A. A
• B. B
• C. C
• D. D

Hint:

When tiling a shape, try rotating the tiles and fitting them together without altering their size or flipping them.

Answer 1

The Correct Option is C, D

Step 1: The tiles must fit perfectly into the triangle without any scaling, repeating, or flipping. After rotation, options C and D correctly fit all tiles into the triangle.
Step 2: Option A and B fail to fit the tiles correctly, as they either leave gaps or exceed the boundaries of the triangle.
Step 3: Therefore, the correct answers are (C) and (D).

Answer 2

The empty triangle needs to be filled exactly using five given tiles, without scaling, repeating, or flipping any of them, though rotation is allowed. Since no tile can be resized or reused, every tile must appear exactly once in the correct rotation, and their combined area and outline must match the triangle exactly with no gaps or overlaps.

1. Option A: The five pieces shown here do not stack into a single triangular outline when rotated; at least one piece leaves a mismatched edge that would create a gap along the triangle's boundary.
2. Option B: Here, one of the pieces would need to be resized smaller or larger than its original shape to close up the outline, which is not allowed since scaling is off the table.
3. Option C: Rotating each of the five pieces here, they slot together edge to edge with no gaps and no overlaps, and the combined outline matches the given triangle exactly.
4. Option D: This grouping leaves a leftover sliver of space uncovered near one corner of the triangle once all five pieces are placed, since one piece's angle does not quite match the triangle's corner there.

Only option C uses all five original tiles, each only rotated and never resized or repeated, to exactly close up the triangle's outline with no leftover gaps.

So the option that exactly fills the triangle is Option C.