Squares and equilateral triangles can form a tiling that has at every vertex:
A) three squares and two triangles.
B) two squares and three triangles.
C) one square and four triangles.
D) one square and five triangles.

Question

Quizplus · Accepted Answer

At every vertex, there must be a total of 5 edges meeting. Each edge belongs to either a square or a triangle. Each square has 4 edges and each triangle has 3 edges. Therefore, the number of squares and triangles at every vertex must satisfy the equation 4x + 3y = 5, where x is the number of squares and y is the number of triangles. The only solution that satisfies this equation with whole numbers and has more triangles than squares is x=2 and y=3, so the answer is B: two squares and three triangles.

Squares and Equilateral Triangles Can Form a Tiling That Has