Question

Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let $B$ be the total area of the blue triangles, $W$ the total area of the white squares, and $R$ the area of the red square. Which of the following is correct?

$B=W$

$W=R$

$B=R$

$3B=2R$

$2R=W$

Answer: A

Concepts:area decomposition congruence (geometry)

Difficulty rating: 1270

Solution:

Divide the flag into congruent right triangles by drawing the grid lines and diagonals. Counting gives $24$ triangles in the blue region, $24$ in the white region, and $16$ in the red region.

Hence $B=W.$

Thus, the correct answer is A.

2002 AMC 10A Problem 8

Answer: A

Difficulty rating: 1270

Solution:

Problem 8 in Other Years