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?
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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.
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