The article presents two intriguing geometry puzzles, focusing on triangle and rectangle configurations. The first problem assesses understanding of degenerate triangles, elucidating how a triangle can collapse into a line segment. The second challenge involves dividing a square into five rectangles under specific conditions, emphasizing the uniqueness of configuration where rectangles don't share sides. Additionally, a second rectangle arrangement must use specific dimensions summing to maintain integrity within an 11x11 area while adhering to integer constraints of side lengths. The article invites reader participation in puzzle creation as well, fostering engagement and community interaction.
The triangle is degenerate, effectively becoming a line, meaning AD, the dashed line, measures 1 due to overlapping sides of lengths that total 8.
Dividing a square into five rectangles without shared sides requires a unique layout, ensuring no two rectangles share an entire side at any point.
For the 11x11 square, you can achieve two configurations by pairing side lengths that sum to 11 and ensuring the area is divided into five distinct rectangles.
Success in these puzzles hinges on recognizing degenerate forms and creatively partitioning areas while adhering to mathematical constraints and conditions.
Collection
[
|
...
]