Library / UKMT Intermediate Mathematical Challenge /144 of 267

UKMT Intermediate Mathematical Challenge, 2026

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows the UKMT logo, which is comprised of three identical parallelograms enclosing an equilateral triangle of side length $Y$ . The ratio of the lengths $X:Y:Z$ is $1:4:5$ . What is the ratio of the area of the enclosed triangle to the total area of the parallelograms?

(A) $1:2$ (B) $3:5$ (C) $5:9$ (D) $8:15$ (E) $1:1$

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.