Maths Olympiad Prep

Library / /216 of 520

Geometry Difficulty 2.9 Junior Find the answer

Suppose a square piece of paper is folded in half vertically. The folded paper is then cut in half along the dashed line. Three rectangles are formed-a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?

Pick one

Solution

From here on, a blue line represents a cut, the dashed line represents the fold.

From the diagram, we can tell the perimeter of one of the small rectangles is 2(4x+x)=10x2(4x+x)=10x and the perimeter of the large rectangle is 2(4x+2x)=12x2(4x+2x)=12x. The desired ratio is 10x12x=5/6E\frac{10x}{12x}=5/6\rightarrow \boxed{\text{E}}

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.