Maths Olympiad Prep

Library / UKMT Intermediate Mathematical Challenge /170 of 267

UKMT Intermediate Mathematical Challenge, 2026

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows an octagon which is formed by two overlapping rectangles. Which of the following is a correct expression for the perimeter of the octagon?

(A) 2p+2r2p + 2r (B) 2p+2q2p + 2q (C) 2q+2r2q + 2r (D) 2p−2q+2r2p - 2q + 2r (E) 2p+2q−2r2p + 2q - 2r

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.