Track / Stage 4 / 233 of 340 #493 of 2000

Problem 493

AMC 12 late, AIME early

Geometry Difficulty 4.9 Find the answer

10. As shown in the figure, the centers of two equilateral triangles coincide, and their three pairs of sides are parallel respectively. If the distance between each pair of sides is $\sqrt{3}$ , then the difference in the side lengths of the two equilateral triangles is ( ).
A. $2 \sqrt{3}$
B. $4 \frac{1}{2}$
C. $3 \sqrt{3}$
D. 6
E. $4 \sqrt{3}$

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.