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MATH / Point P is inside equilateral triangle ABC such that the altitudes from P to (AB)¯, (BC)¯, and (CA)¯ have lengths 5, 6, and 7 respectively. What is the area of triangle ABC?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Point PP is inside equilateral triangle ABCABC such that the altitudes from PP to AB¯\overline{AB}, BC¯\overline{BC}, and CA¯\overline{CA} have lengths 5, 6, and 7 respectively. What is the area of triangle ABCABC?
Plain-text mathematical notation (without MathML)
Point P is inside equilateral triangle ABC such that the altitudes from P to (AB)¯, (BC)¯, and (CA)¯ have lengths 5, 6, and 7 respectively.  What is the area of triangle ABC?
Original LaTeX notation
Point $P$ is inside equilateral triangle $ABC$ such that the altitudes from $P$ to $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$ have lengths 5, 6, and 7 respectively.  What is the area of triangle $ABC$?

level

Level 5

type

Geometry

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Source and history

task_id
8ef1e14f-6fa2-58b9-beb8-ff54526b812d
task_key
geometry--test--8ef1e14f-6fa2-58b9-beb8-ff54526b812d
task_revision_id
1
config / split
geometry / test

Official source

initial import