Question

If $\frac{AD}{BD}=\frac{3}{5}$, AC = 14 cm and $DE\parallel BC$ Find EC.

• A. 8
• B. 4.5
• C. 8.75
• D. 3

Answer 1

The correct option is C

8.75

It is given that $\frac{AD}{BD}$ = $\frac{3}{5}$

$\because DE\parallel BC,\text{In}△ADE\text{and}△ABC,$

$\angle$ADE = $\angle$ABC [corresponding angles]

$\angle DAE=\angle BAC$ [common angle]
Since two angles are equal, it follows that the third angle is also correspondingly equal and hence the triangles are similar.

$\therefore \frac{AD}{BD}=\frac{AE}{EC}=\frac{3}{5}$

$\frac{EC}{AC}=\frac{5}{8}$
$EC=\frac{5}{8}\times AC$
$EC=\frac{5}{8}\times 14=8.75cm$