Question

in triangle ABC,AB=8,BC=7and CA=6 and side BC is extended shown in the figure to a point P so that triangle PAB Congress PCA.Find length of PC?

Answer 1

what is your answer of this question

Answer 2

Answer:

PC = 9.

Step-by-step explanation:

From the given similarity,

PA/PC = PB/PA = AB/AC = 8/6 = 4/3

Cross multiplying to get a system of equations in PA and PC, we get

3PA = 4PC and

4PA = 3PB = 3(PC + 7) = 3PC + 21

Multiplying the first equation by 4 on both sides and multiplying the second equation by 3, (we do this so that we can eliminate PA and have an equation in terms of PC, which we want)

12PA = 16PC and

12PA = 9PC + 63

After subtracting the second equation from the first and solving for PC,

7PC - 63 = 0

       7PC = 63

         PC = 9

Therefore PC = 9.