Cool 3-D problem

Geometry Level pending

Feet of the perpendicular drawn from the point P ( 2 , 3 , 5 ) P(2,3,-5) on the axes of coordinate are A , B A,B and C C . The area of A B C \triangle ABC is a b units \dfrac{a}{b} \text{ units} . Then what is the value of a + b a+b ?

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The answer is 21.

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