In a triangle ABC, D and E are points on BC such that AD= AE and ∠BAD = ∠CAE . If AB = (2p + 3 ), BD = 2p, AC = ( 3q - 1 ) andCE = q , then find the value of ( p + q ).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 3
In triangles ABC, ABD, and AEC
Two angles and one side are similar so ABD ≅ AEC
now AB/AC = BD/CE = AD/AE
(2p + 3 )/ ( 3q - 1 ) = 2p/q = 1 (∵ AD = AE )
(2p + 3 ) /( 3q - 1 ) = 1 →i
2pq = 1 →ii
put the value of equation (ii) in (i)
we get p = 1
q = 2
so p+q = 2+1= 3