Maths Olympiad Prep

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Geometry Difficulty 2.0 Junior Find the answer

Rectangle ABCDABCD, pictured below, shares 50%50\% of its area with square EFGHEFGH. Square EFGHEFGH shares 20%20\% of its area with rectangle ABCDABCD. What is ABAD\frac{AB}{AD}?

Pick one

Solution

If we shift AA to coincide with EE, and add new horizontal lines to divide EFGHEFGH into five equal parts:

This helps us to see that AD=a/5AD=a/5 and AB=2aAB=2a, where a=EFa=EF.
Hence ABAD=2aa/5=10\dfrac{AB}{AD}=\dfrac{2a}{a/5}=10.

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