( A B = a ) and ( A C = b ) are the sides of ( a A B C . P ) is a point on ( A B ) and (Q ) is a point on ( B C ) such that ( A P P B = 1 2 ) and ( B Q Q C = 1 2 ). If the point of intersection of ( A Q ) and ( C P ) is (D ) and the area of

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( A B = a ) and ( A C = b ) are the sides of ( a A B C . P ) is a point on ( A B ) and (Q ) is a point on ( B C ) such that ( A P P B = 1 2 ) and ( B Q Q C = 1 2 ). If the point of intersection of ( A Q ) and ( C P ) is (D ) and the area of ( B C D ) is 7 square units, then the area of the ( A B C ) (in the same sq units) is

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Correct answer: A. ( 49 4 )

According to given informations, ( A P = a 3 and A Q = 2 a + b 3 ) Let (D ) divides the line ( A Q ) in ratio ( : 1 ) and ( C P ) in ( : 1 ). So, ( = (2 a + b ) 3( +1) = a 3 + b +1 ) On comparing ( array rlrl & & 3( +1) & = 2 3( +1) and 1 +1 = 3( +1) & 3( +1) & = 2 +1 =6 So, & 1 7 & = 3( +1) 3 +3=7 = 3 4 & & AD & = 2 a+ b 7 array ) So, ( 1 7 = 3( +1) 3 +3=7 = 3 4 ) ( A D = 2 a + b 7 ) Now area of ( B C D= 1 2 | B C B D | ) ( aligned & = 1 2 |( b - a ) ( b -5 a 7 ) | & = 1 14 |(- b a )-( a b )| & = 4 14 | a b |=7 (g

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