2002 AMC 10A Problem 8

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

Cut the whole flag into congruent right triangles

Count how many of those congruent triangles fill each color

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.

Problem 8 in other years