Question

In the given figure, $DE\parallel BC$ and $BD=DC$ If $AD=4.5cm,AE=3.9cm$ and $DC=7.5cm$, find $CE$.

• A. $6.5cm$
• B. $5.5cm$
• C. $8.5cm$
• D. $7.5cm$

Answer 1

Answer: (A)

$6.5cm$

Given: $DE\parallel BC$, $BD=DC$

Now, In $△ADE$ and $△ABC$,

$\angle DAE=\angle BAC$ (Common angle)

$\angle ADE=\angle ABC$ (Corresponding angles)

$\angle AED=\angle ACB$ (Corresponding angles)

$△ADE\sim △ABC$ (AAA rule)

thus, $\frac{AD}{AB}=\frac{AE}{AC}$ (Corresponding sides)

$\frac{AD}{AD+BD}=\frac{AE}{AE+EC}$

$\frac{AD}{AD+CD}=\frac{AE}{AE+EC}$

$\frac{4.5}{4.5+7.5}=\frac{3.9}{3.9+CE}$

$3.9+CE=\frac{3.9\times 12}{4.5}$

$3.9+CE=10.4$

$\therefore CE=6.5$ cm