AMC10 2002 A

AMC10 2002 A · Q8

AMC10 2002 A · Q8. It mainly tests Triangles (properties), Area & perimeter.

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?

Betsy设计了一面旗帜，使用蓝色三角形、小白色方块和一个红色中心方块，如图所示。设 $B$ 为蓝色三角形的总面积，$W$ 为白色方块的总面积，$R$ 为红色方块的面积。以下哪个正确？

(A) $B = W$ $B = W$

(B) $W = R$ W = R

(D) 3$B$ = 2$R$ 3B = 2R

(E) 2$R$ = $W$ 2R = W

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) Draw additional lines to cover the entire figure with congruent triangles. There are 24 triangles in the blue region, 24 in the white region, and 16 in the red region. Thus, $B=W$.

（A）画出额外的线段，用全等三角形覆盖整个图形。蓝色区域有 24 个三角形，白色区域有 24 个，红色区域有 16 个。因此，$B=W$。

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