In ΔDEF, DF = 8.4 cm, EF = 14 cm. P is a point on DE such that FP = 11.2 cm and ∠DFP = ∠E. What is the length (in cm) of EP ?
Answer & explanation
Correct answer: option 3
On comparing ΔDFP and ΔDEF
\(\frac{DF}{DE}\) = \(\frac{PF}{EF}\) ⇒ \(\frac{8.4}{DE}\) = \(\frac{11.2}{14}\)
DE = 10.5 cm
Again
\(\frac{DP}{DF}\) = \(\frac{PF}{EF}\) ⇒ \(\frac{DP}{8.4}\) = \(\frac{11.2}{14}\)
⇒ DP = \(\frac{(11.2 × 8.4)}{14}\) = 6.72
∴ EP = DE - DP = 10.5 - 6.72 = 3.78 cm