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MATH / In triangle ABC, the length of side (BC)¯ is equal to the average of the other two sides. Also, cosC=(AB)/(AC).Given that all the side lengths are integers, find the smallest possi…

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problem

In triangle ABC,ABC, the length of side BC¯\overline{BC} is equal to the average of the other two sides. Also, cosC=ABAC.\cos C = \frac{AB}{AC}.Given that all the side lengths are integers, find the smallest possible area of triangle ABC.ABC.
Plain-text mathematical notation (without MathML)
In triangle ABC, the length of side (BC)¯ is equal to the average of the other two sides.  Also,
cosC=(AB)/(AC).Given that all the side lengths are integers, find the smallest possible area of triangle ABC.
Original LaTeX notation
In triangle $ABC,$ the length of side $\overline{BC}$ is equal to the average of the other two sides.  Also,
\[\cos C = \frac{AB}{AC}.\]Given that all the side lengths are integers, find the smallest possible area of triangle $ABC.$

level

Level 4

type

Precalculus

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Source and history

task_id
2b323bcc-093d-5858-a83f-356ef1dc1882
task_key
precalculus--test--2b323bcc-093d-5858-a83f-356ef1dc1882
task_revision_id
1
config / split
precalculus / test

Official source

initial import