Question

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

Calculate: (i) EF (ii) AC

• A. EF = 12.5 cm, AC = 35.5 cm
• B. EF = 13.5 cm, AC = 37.5 cm
• C. EF = 13.5 cm, AC = 32 cm
• D. EF = 14 cm, AC = 37.5 cm

Answer 1

The correct option is B

EF = 13.5 cm, AC = 37.5 cm

In the given figure.

AB||EF||CD

AB =22.5 cm, EP=7.5 cm

PC =15 cm and DC =27 cm

To calculate: (i) EF (ii)AC

In $\Delta DCP$ and $\Delta PEF$

$\angle CPD=\angle EPF$ (Vertically opp. angles)

$\angle DCP=\angle PEF$ (Alternate angles)

$\therefore \Delta DCP\sim \Delta PEF$ (AA axiom)

$\therefore \frac{DC}{EF}=\frac{CP}{PE}\Rightarrow \frac{27}{EF}=\frac{15}{7.5}$

$\Rightarrow EF=\frac{27\times 7.5}{15}=\frac{27}{2}=13.5cm$

Similarly in $\Delta ABC,EF||AB$

$\therefore \Delta CDF\sim \Delta ACB$

$\therefore \frac{CE}{AC}=\frac{EF}{AB}$

$\frac{22.5}{AC}=\frac{13.5}{22.5}$

$AC=\frac{22.5\times 22.5}{13.5}$

$=\frac{225\times 225}{135\times 10\times 10}=\frac{375}{10}cm$

$\therefore AC=37.5cm$