{"status": "success", "data": {"description_md": "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 $\\triangle ABC$?\n\n$\\textbf{(A)}\\ 9\\qquad\\textbf{(B)}\\ 16\\qquad\\textbf{(C)}\\ 25\\qquad\\textbf{(D)}\\ 36\\qquad\\textbf{(E)}\\ 37$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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 ?

\\textbf{(A)}\\ 9\\qquad\\textbf{(B)}\\ 16\\qquad\\textbf{(C)}\\ 25\\qquad\\textbf{(D)}\\ 36\\qquad\\textbf{(E)}\\ 37

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2017 AMC 12B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12B_p16", "prev": "/problem/17_amc12B_p14"}}