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 ?

3.78

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