MathLabs

Problem 5

Show that for every integer n>=6 there exists a convex hexagon that can be dissected into exactly n congruent triangles.
Step 1 of 4: Set up congruent right-triangle blocks
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T(p,q): a right triangle with legs p,q;L1,L2,M,R1,R2 are the five standard blocks.T(p,q):\text{ a right triangle with legs }p,q;\quad L_1,L_2,M,R_1,R_2\text{ are the five standard blocks.}
Detailed analysis

Take the basic building block to be a right triangle with integer legs p and q. The official solution arranges copies into five boundary blocks L_1,L_2,M,R_1,R_2; adjoining boundaries have equal lengths, and the outer boundary is convex when the indicated combinations are used.