Question

In the given figure, EF || AD and ED || AC. if BF = 4 cm, FD = 6 cm and BE = 8 cm, then BC = _______

• A. 12 cm
• B. 15 cm
• C. 25 cm
• D. None

Answer 1

The correct option is C 25 cm

In $\Delta$ BDA we have EF || AD
$\therefore \frac{BD}{FD}=\frac{BE}{EA}\Rightarrow \frac{4}{6}=\frac{8}{EA}$
$\Rightarrow EA=12cm$
in $\Delta$ ABC we have ED|| AC
$\therefore \frac{BD}{BC}=\frac{BE}{BA}\Rightarrow \frac{BF+FD}{BC}=\frac{BE}{BE+EA}$
$\Rightarrow \frac{4+6}{BC}=\frac{8}{8+12}$
$\Rightarrow BC=\frac{10\times 20}{8}=25cm$