Problem

Problem of the Day #73

POTD February 19, 2024

Let $ABCD$ be a tetrahedron such that edges $AB$ , $AC$ , and $AD$ are mutually perpendicular. Let the areas of triangles $ABC$ , $ACD$ , and $ADB$ be denoted $5$ , $6$ , and $7$ , respectively. If the area of triangle $BCD$ can be written as $\sqrt{a}$ where $a$ is a positive integer, find $a$ .

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Category: Problem of the Day
Points: 4
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