Question

In the given figure $AB\parallel EF\parallel DC$; AB = 67.5 cm. DC = 40.5 cm and AE = 52.5 cm. Find the length of EC.

• A. EC = 24.4 cm
• B. EC = 70.6 cm
• C. EC = 45.7 cm
• D. EC = 31.5 cm

Answer 1

The correct option is D

EC = 31.5 cm

(i) In the figure

$\because AB\parallel EF\parallel DC$

$\therefore$ There are three pairs of similar triangles

(i) $\Delta AEB\sim \Delta DEC$

(ii) $\Delta ABC\sim \Delta EFC$

(iii) $\Delta AEB\sim \Delta DEC$

$\therefore \frac{AE}{EC}=\frac{BE}{ED}=\frac{AB}{DC}$

But AB = 67.5 cm, DC = 40.5 cm and AE = 52.5 cm

$\therefore \frac{52.5}{EC}=\frac{67.5}{40.5}=EC\times 67.5=52.5\times 40.5$

$EC=\frac{52.5\times 40.5}{67.5}=31.5\text{cm}$