Library / UKMT Pink Kangaroo /145 of 220

UKMT Pink Kangaroo, 2024

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

Sadinie is asked to create a rectangular enclosure using $40$ m of fencing so that the side-lengths, in metres, of the enclosure are all prime numbers. What is the maximum possible area of the enclosure?

(A) $51\text{ m}^2$ (B) $84\text{ m}^2$ (C) $91\text{ m}^2$ (D) $96\text{ m}^2$ (E) $99\text{ m}^2$

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.