Library / UKMT Junior Mathematical Challenge /163 of 274

UKMT Junior Mathematical Challenge, 2017

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The small trapezium on the right has three equal sides and angles of $60^\circ$ and $120^\circ$ . Nine copies of this trapezium can be placed together to make a larger version of it, as shown. The larger trapezium has perimeter 18 cm. What is the perimeter of the smaller trapezium?

(A) $2\text{ cm}$ (B) $4\text{ cm}$ (C) $6\text{ cm}$ (D) $8\text{ cm}$ (E) $9\text{ cm}$

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.