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Source: 2017 AMC 10B #19, 12B #15

February 16, 2017

ratiogeometryAMCAMC 10AMC 10 B2017 AMC 10B2017 AMC 12B

Problem Statement

Let

ABC

be an equilateral triangle. Extend side

\overline{AB}

beyond

B

to a point

B'

so that

BB' = 3AB

. Similarly, extend side

\overline{BC}

beyond

C

to a point

C'

so that

CC' = 3BC

, and extend side

\overline{CA}

beyond

A

to a point

A'

so that

AA' = 3CA

. What is the ratio of the area of

\triangle A'B'C'

to the area of

\triangle ABC

?

<span class='latex-bold'>(A) </span>9:1\qquad<span class='latex-bold'>(B) </span>16:1\qquad<span class='latex-bold'>(C) </span>25:1\qquad<span class='latex-bold'>(D) </span>36:1\qquad<span class='latex-bold'>(E) </span>37:1

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