Question

In the figure, $AB,EFandCD$ are parallel lines. Given that $AB=15cm,EG=5cm,GC=10cmandDC=18cm$. Find $EFandAC$ respectively.

• A. $9,25$
• B. $25,9$
• C. $16,25$
• D. $25,16$

Answer 1

The correct option is A $9,25$

In $\Delta EFG$ and $\Delta CDG,$ we can see,

$\angle EGF=\angle CGD$ (vertically opp.$\angle s$).

$\angle EFG=\angle CDG$ (corresponding $\angle s$).

$\angle GEF=\angle GCD$ (corresponding $\angle s$).

Hence,$\Delta EFG$ similar to $\Delta CDG.$

By applying property of similarity

$\frac{EF}{EG}=\frac{DC}{CG}\Rightarrow \frac{EF}{5}=\frac{18}{10}$

$\Rightarrow EF=9cm$

Now in $\Delta ABC$ and $\Delta EFC.$

$\angle ACB=\angle ECF$ (common angle)

$\angle CEF=\angle CAB$ (corresponding angles)

$\angle CFE=\angle CBA$ (corresponding angles)

$\frac{AC}{AB}=\frac{EC}{EF}$

$\Rightarrow \frac{AC}{15}=\frac{15}{9}$

$\Rightarrow AC=25cm$

(A) 9,25 is the answer.