Library / UKMT Intermediate Mathematical Challenge /234 of 267

UKMT Intermediate Mathematical Challenge, 2019

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows six congruent equilateral triangles, of side-length $2$ , placed together to form a parallelogram. What is the length of $PR$ ?

(A) $2\sqrt{13}$ (B) $7$ (C) $6\sqrt{3}$ (D) $9$ (E) $7\sqrt{3}$

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.