Competition problem — Geometry — Maths Olympiad Prep

Library / /24 of 80

Geometry Difficulty 4.6 AIME Prove it North Macedonia

A square shaped orchard with side length $26\text{m}$ is fenced in with $3$ rows of wire. Is it possible with the same wire to fence in a rectangular shaped orchard with side lengths $95\text{m}$ and $60\text{m}$ ?

Solution

For fencing in the square shaped orchard $3 \cdot 4 \cdot 26\text{m} = 312\text{m}$ of wire is used. To fence in the rectangular orchard $2 \cdot (95\text{m} + 60\text{m}) = 310\text{m}$ of wire is needed. So the answer is affirmative.

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: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.