You are asked to find the area of a rectangle and are given two facts. Fact I: its perimeter is 30 cm. Fact II: its length is twice its breadth. Which statement about these facts is correct?

Fact I alone leaves the length and breadth adding to 15 cm, which allows 1 by 14, 5 by 10, 7 by 8 and many more — all with different areas. Fact II alone gives a shape but no size at all. Put together they pin things down: breadth $b$ and length $2b$ give $2(b+2b)=30$, so $6b=30,b=5$ cm, length 10 cm and area 50 square cm. The trap is 'Fact I on its own', chosen because a perimeter feels like a full measurement, but a perimeter fixes only the sum of the two sides, never the area.