Library / UKMT Junior Mathematical Challenge /260 of 274

UKMT Junior Mathematical Challenge, 2018

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The shapes $P$ and $Q$ are formed from two and three identical rectangles, respectively. Their perimeters are 58 cm and 85 cm respectively. What is the perimeter of one of the rectangles?

(A) $30\text{ cm}$ (B) $31\text{ cm}$ (C) $32\text{ cm}$ (D) $33\text{ cm}$ (E) $34\text{ cm}$

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.