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Omni-MATH / Tetrahedron ABCD has side lengths AB=6,BD=6√(2),BC=10,AC=8,CD=10, and AD=6. The distance from vertex A to face BCD can be written as (a√(b))/(c), where a,b,c are positive integers,…

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problem

Tetrahedron ABCDA B C D has side lengths AB=6,BD=62,BC=10,AC=8,CD=10A B=6, B D=6 \sqrt{2}, B C=10, A C=8, C D=10, and AD=6A D=6. The distance from vertex AA to face BCDB C D can be written as abc\frac{a \sqrt{b}}{c}, where a,b,ca, b, c are positive integers, bb is square-free, and gcd(a,c)=1\operatorname{gcd}(a, c)=1. Find 100a+10b+c100 a+10 b+c.
Plain-text mathematical notation (without MathML)
Tetrahedron ABCD has side lengths AB=6,BD=6√(2),BC=10,AC=8,CD=10, and AD=6. The distance from vertex A to face BCD can be written as (a√(b))/(c), where a,b,c are positive integers, b is square-free, and gcd(a,c)=1. Find 100a+10b+c.
Original LaTeX notation
Tetrahedron $A B C D$ has side lengths $A B=6, B D=6 \sqrt{2}, B C=10, A C=8, C D=10$, and $A D=6$. The distance from vertex $A$ to face $B C D$ can be written as $\frac{a \sqrt{b}}{c}$, where $a, b, c$ are positive integers, $b$ is square-free, and $\operatorname{gcd}(a, c)=1$. Find $100 a+10 b+c$.

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Source and history

task_id
e5e2e6d5-0a4d-57de-a91a-5d66d9b7f25e
task_key
test--e5e2e6d5-0a4d-57de-a91a-5d66d9b7f25e
task_revision_id
1
config / split
/ test

Official source

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