Question

In the given figure, Suppose AB, AC and BC have lengths 13 cm, 14 cm and 15 cm respectively. If $\frac{AF}{FB}=\frac{3}{8}and\frac{CE}{EA}=\frac{6}{9}$, then find BD and DC.

• A. 8 cm and 7 cm
• B. 10 cm and 5 cm
• C. 12 cm and 3 cm
• D. 9 cm and 6 cm

Answer 1

The correct option is C 12 cm and 3 cm

Given that AB = 13 , AC = 14 and BC = 15 .
Let BD = x cm and DC = y cm.Using Ceva’s theorem, we have,
$\frac{AF}{FB}\times \frac{CE}{EA}\times \frac{BD}{DC}=1$ ... (1)
Substitute the values of $\frac{AF}{FB}=\frac{3}{8}and\frac{CE}{EA}=\frac{6}{9}$ in (1),
we have, $\frac{3}{8}\times \frac{6}{9}\times \frac{x}{y}=1$
$\frac{x}{y}\times \frac{1}{4}=1$
Hence, x = 4y ... (2)
BC = BD + DC = 15 so, x + y = 15 ... (3)
From (2), using x = 4y in (3),
we get, 4y + y = 15
5y = 15 then y = 3
Substitute y = 3 in (3) we get, x = 12 . Hence BD = 12 cm , DC = 3 cm.