Library / UKMT Grey Kangaroo /190 of 242

UKMT Grey Kangaroo, 2020

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

The pattern on a large square tile consists of eight congruent right-angled triangles and a small square. The area of the tile is $49\text{ cm}^2$ and the length of the hypotenuse $PQ$ of one of the triangles is $5\text{ cm}$ . What is the area of the small square?

(A) $1\text{ cm}^2$ (B) $4\text{ cm}^2$ (C) $9\text{ cm}^2$ (D) $16\text{ cm}^2$ (E) $25\text{ cm}^2$

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.