In $\triangle$ ABC, D and E are the points on sides AC and BC, respectively such that DE parallel to AB. F is a point on CE such that DF $\perp$ CE. If CE = 6 cm, and CF = 2.5 cm, then BC is equal to:
Answer & explanation
Correct answer: option 1
In triangle ABC ,
\(\frac{CE}{CB}\) = \(\frac{CD}{CA}\)
\(\frac{6}{CB}\) = \(\frac{CD}{CA}\) ----(1)
In triangle AEC,
\(\frac{CF}{CE}\) = \(\frac{CD}{CA}\)
\(\frac{2.5}{6}\) = \(\frac{CD}{CA}\)
\(\frac{5}{12}\) = \(\frac{CD}{CA}\)
By using equation 1 ,
\(\frac{6}{CB}\) = \(\frac{5}{12}\)
BC = 14.4 cm