Question

In the figure given below, $CD\parallel EF\parallel AB$. If $AB=22.5$ cm, $EP=7.5$ cm, $PC=15$ cm and $DC=27$ cm. Calculate $EF$.

• A. $EF=14.5cm$
• B. $EF=13.5cm$
• C. $EF=12.5cm$
• D. None of the above

Answer 1

Answer: (B)

$EF=13.5cm$

Given: $CD\parallel EF\parallel AB$

In $△DCP$ and $△PEF$,
$\angle DPC=\angle EPF$ (Vertically opposite angles)
$\angle DCP=\angle PEF$ (Alternate angles for parallel lines CD and EF)
$\angle CDP=\angle PFE$ (Alternate angles for parallel lines CD and EF)

Thus, $△DCP\sim △FEP$ (AAA rule)

Hence, $\frac{DC}{EF}=\frac{PC}{EP}$ (Corresponding sides)

$\frac{27}{EF}=\frac{15}{7.5}$

$EF=13.5$ cm