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MATH / Equiangular hexagon ABCDEF has side lengths AB=CD=EF=1 and BC=DE=FA=r. The area of triangle ACE is 70% of the area of the hexagon. What is the sum of all possible values of r?

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problem

Equiangular hexagon ABCDEFABCDEF has side lengths AB=CD=EF=1AB=CD=EF=1 and BC=DE=FA=rBC=DE=FA=r. The area of triangle ACEACE is 70%70\% of the area of the hexagon. What is the sum of all possible values of rr?
Plain-text mathematical notation (without MathML)
Equiangular hexagon ABCDEF has side lengths AB=CD=EF=1 and BC=DE=FA=r. The area of triangle ACE is 70% of the area of the hexagon. What is the sum of all possible values of r?
Original LaTeX notation
Equiangular hexagon $ABCDEF$ has side lengths $AB=CD=EF=1$ and $BC=DE=FA=r$. The area of triangle $ACE$ is $70\%$ of the area of the hexagon. What is the sum of all possible values of $r$?

level

Level 2

type

Precalculus

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Source and history

task_id
92a0f1af-dbfe-5390-8257-4fc39719b08b
task_key
precalculus--test--92a0f1af-dbfe-5390-8257-4fc39719b08b
task_revision_id
1
config / split
precalculus / test

Official source

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