Let ABCD be a tetrahedron such that the edges AB,AC and AD are mutually perpendicular. Let the area of triangles ABC,ACD and ADB be $$3$$,$$4$$ and $$5$$ sq. units respectively. Then the area of the triangle BCD is :

Question

Let ABCD be a tetrahedron such that the edges AB,AC and AD are  mutually perpendicular. Let the area of triangles ABC,ACD and ADB be $$3$$,$$4$$ and $$5$$ sq. units respectively. Then the area of the triangle BCD is :

Infinity Learn · Accepted Answer

Area of $$ABCD=12$$|BC→XBD→| $$=12$$  $$cj^$$ $$-bi$$∧  $$dk^-bi$$∧ $$=12$$ |dci∧ $$+$$ bck∧ $$+$$ bdj∧  | $$=12$$ $$b2c2$$ $$+$$ $$c2d2$$ $$+$$ $$d2b2$$                                               X $$($$ Now  $$6=bc$$;  $$8=cd$$;  $$10=bd$$ $$b2c2+c2d2=d2b2=200$$  Substituting the value in eqn. (i),  $$A=12200$$ $$=$$  $$52$$

$Let A B C D be a tetrahedron such that the edges A B, A C and A D are$
$mutually perpendicular. Let the area of triangles ABC, ACD and ADB be 3, 4 and$
$5 sq. units respectively. Then the area of the triangle BCD is :$

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Let ABCD be a tetrahedron such that the edges AB,AC and AD are mutually perpendicular. Let the area of triangles ABC,ACD and ADB be 3,4 and 5 sq. units respectively. Then the area of the triangle BCD is :

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Ready to Test Your Skills?

free study material

$Let A B C D be a tetrahedron such that the edges A B, A C and A D are$
$mutually perpendicular. Let the area of triangles ABC, ACD and ADB be 3, 4 and$
$5 sq. units respectively. Then the area of the triangle BCD is :$