In the following figure, AD bisects angles BAC. Find the length (in cm) of BD.
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 4
AD bisects angle BAC.
Here, in ΔPQR, PL bisects ∠RPQ.
According to the Angle Bisector Theorem -
RL/LQ = PR/PQ
According to the concept -
[6/(2x - 3)] = [(x - 2)/x]
6x = 2x2 - 4x - 3x + 6
6x = 2x2 - 7x + 6
0 = 2x2 - 7x + 6 - 6x
2x2 - 13x + 6 = 0
2x2 - 12x - x + 6 = 0
2x(x - 6) - 1(x - 6) = 0
(x - 6)(2x - 1) = 0
x = 6, 1/2
For x = 1/2 -
BD = 1/2 - 2 = - 3/2 (As the value of a side cannot be negative)
x = 6
BD = 6 - 2 = 4 cm