v12345 wrote:
In a triangle ABC, AB=8, BC=7 and CA=6. Extend BC to P such that △PAB is similar to △PCA, then the length of PC is
A. 2
B. 5
C. 6
D. 9
E. 12
From similar triangles, we have \(\frac{PA}{PC} = \frac{PB}{PA} = \frac{AB}{CA}\).
Set PC = 7. Then from \(\frac{PA}{PC} = \frac{PB}{PA}\), we can find \(PA^2 = PC*PB = x*(x + 7)\) then \(PA = \sqrt{x*(x + 7)}\).
Finally from \(\frac{PA}{AB} = \frac{PC}{CA}\) we can get \(\frac{\sqrt{x*(x+ 7)}}{8} = \frac{x}{6}\).
\(x*(x + 7) = \frac{16}{9}*x^2\)
\(7x = \frac{7}{9}x^2\)
\(x = 7*\frac{9}{7} = 9\) is one solution.
Ans: D
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to
guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the
fastest in the world. Feel free to
reach out!