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2017 AMC 10B Problem 19

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2017 AMC 10B Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Triangles: Area & Pythagorean · difficulty 4 of 5 · about 5 min · position P16-20

Let $ABC$ be an equilateral triangle. Extend side $\overline{AB}$ beyond $B$ to a point $B'$ so that $BB'=3 \cdot AB$ . Similarly, extend side $\overline{BC}$ beyond $C$ to a point $C'$ so that $CC'=3 \cdot BC$ , and extend side $\overline{CA}$ beyond $A$ to a point $A'$ so that $AA'=3 \cdot CA$ . What is the ratio of the area of $\triangle A'B'C'$ to the area of $\triangle ABC$ ?

A)
$9:1$
B)
$16:1$
C)
$25:1$
D)
$36:1$
E)
$37:1$

2017 AMC 10B Problem 19

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