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ABCD is a tetrahedron such that each of ...

ABCD is a tetrahedron such that each of the `triangleABC`, `triangleABD` and `triangleACD` has a right angle at A. If `ar(triangleABC) = k_(1). Ar(triangleABD)= k_(2), ar(triangleBCD)=k_(3)` then `ar(triangleACD)` is

A

`sqrt(k_(1)^(2)+k_(2)^(2)+k_(3)^(2))`

B

`sqrt((k_(1)k_(2)k_(3))/(k_(1)+k_(2)+k_(3))`

C

`sqrt(|k_(1)^(2)+k_(2)^(2)-k_(3)^(2)|)`

D

`sqrt(|k_(2)^(2)-k_(1)^(2)-k_(3)^(2)|)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let us suppose that A is origin .
`ar(triangleABC)^(2)+ar(triangleACD)^(2)+ar(triangleABD)^(2) =ar(triangleBCD)^(2)`
`rArr ar(triangleACD) = sqrt(|k_(1)^(2)+k_(2)^(2)-k_(3)^(2))|`
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