Library / UKMT Intermediate Mathematical Challenge /180 of 267

UKMT Intermediate Mathematical Challenge, 2018

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows two equilateral triangles. The distance from each point of the smaller triangle to the nearest point of the larger triangle is $\sqrt{3}$ , as shown. What is the difference between the lengths of the edges of the two triangles?

(A) $2\sqrt{3}$ (B) $4\frac{1}{2}$ (C) $3\sqrt{3}$ (D) $6$ (E) $4\sqrt{3}$

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.