Question

In the given figure, AB || EF || CD. If AB = 22.5 cm, EP = 7.5 cm, PC = 15

cm and DC = 27 cm. If EF$=\frac{m}{2}$, Find $m$

Answer 1

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