In ΔABC, DE || AB, where D and E are points on sides AC and BC, respectively. F is a point between C and D such that EF || BD. If AD = 15 cm, DC = 10 cm, then length of CF is :
Answer & explanation
Correct answer: option 3
It is given that :-
AD = 15 cm and DC = 10 cm
In triangle ABC and CDE
\(\frac{CD}{AD}\) = \(\frac{CE}{CB}\) = \(\frac{CD}{CD + AD}\)
\(\frac{CD}{AD}\) = \(\frac{CE}{CB}\) = \(\frac{10}{10 + 15}\)
\(\frac{CD}{AD}\) = \(\frac{CE}{CB}\) = \(\frac{10}{25}\)
\(\frac{CD}{AD}\) = \(\frac{CE}{CB}\) = \(\frac{2}{5}\)
In triangle CFE and CDB
\(\frac{CF}{CD}\) = \(\frac{CE}{CB}\)
{ We know, \(\frac{CE}{CB}\) = \(\frac{2}{5}\) }
\(\frac{CF}{CD}\) = \(\frac{2}{5}\)
\(\frac{CF}{10}\) = \(\frac{2}{5}\)
CF = 4 cm