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MATH / In a three-dimensional coordinate system with origin O, points A, B, and C are on the x-, y-, and z-axes, respectively. If the areas of triangles OAB, OAC, and OBC are 4, 6, and 12…

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problem

In a three-dimensional coordinate system with origin O,O, points A,A, B,B, and CC are on the xx-, yy-, and zz-axes, respectively. If the areas of triangles OAB,OAB, OAC,OAC, and OBCOBC are 4, 6, and 12, respectively, compute the area of triangle ABC.ABC.
Plain-text mathematical notation (without MathML)
In a three-dimensional coordinate system with origin O, points A, B, and C are on the x-, y-, and z-axes, respectively.   If the areas of triangles OAB, OAC, and OBC are 4, 6, and 12, respectively, compute the area of triangle ABC.
Original LaTeX notation
In a three-dimensional coordinate system with origin $O,$ points $A,$ $B,$ and $C$ are on the $x$-, $y$-, and $z$-axes, respectively.   If the areas of triangles $OAB,$ $OAC,$ and $OBC$ are 4, 6, and 12, respectively, compute the area of triangle $ABC.$

level

Level 3

type

Precalculus

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Source and history

task_id
8104edcb-ff87-5e84-8ffe-f34ee9693a54
task_key
precalculus--test--8104edcb-ff87-5e84-8ffe-f34ee9693a54
task_revision_id
1
config / split
precalculus / test

Official source

initial import