Question

In the given figure, $\Delta ABC\sim \Delta ADE$. If AE : EC = 4 : 7 and DE = 6.6 cm, then the length of BC is

• A. $17.75\text{cm}$
• B. $18.15\text{cm}$
• C. $18.30\text{cm}$
• D. $17.30\text{cm}$

Answer 1

The correct option is B

$18.15\text{cm}$

In the given figure,

$\Delta ABC\sim \Delta ADE$

AE : EC = 4 : 7, DE = 6.6 cm, BC = ?

Draw $AL\perp DE$ and $AM\perp BC$ and AL = x cm

We shall find AM in terms of x.

Since $\Delta ADE\sim \Delta ABC$, we have,

$\frac{AE}{AC}=\frac{DE}{BC}$

$\therefore \frac{AE}{AC}=\frac{AE}{AE+EC}=\frac{4}{4+7}=\frac{4}{11}$

$\therefore \frac{DE}{BC}=\frac{AE}{AC}\Rightarrow \frac{4}{11}=\frac{6.6}{BC}$

$\Rightarrow BC=\frac{6.6\times 11}{4}=\frac{36.3}{2}=18.15\text{cm}$