Question

In the given figure $AB,EF$ and $CD$ are parallel lines Given that $EG=5cm,GC=10$ and $DC=18$ cm, then $EF=$

• A. $9$ cm
• B. $25$ cm
• C. $13$ cm
• D. $16$ cm

Answer 1

The correct option is A $9$ cm

In $△GEF$ and $△GCD$

$\Rightarrow$ $\angle EFG=\angle GDC$ [ Alternative angle ]

$\Rightarrow$ $\angle EFG=\angle CGD$ [ Vertically opposite angles ]

$\therefore$ $△GEF\sim △GCD$ [ By $AA$ property ]

Thus,

$\Rightarrow$ $\frac{GE}{CG}=\frac{EF}{CD}$

$\Rightarrow$ $\frac{5}{10}=\frac{EF}{18}$

$\Rightarrow$ $EF=\frac{5}{10}\times 18$

$\therefore$ $EF=9cm$