Library / UKMT Senior Mathematical Challenge /132 of 212

UKMT Senior Mathematical Challenge, 2022

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows two symmetrically placed squares with sides of length $2$ and $5$ . What is the ratio of the area of the small square to that of the shaded region?

(A) $7:24$ (B) $1:3$ (C) $8:25$ (D) $8:21$ (E) $2:5$

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.