Question

Let $△ABC\sim △DEF$ and their areas be, respectively $64{cm}^2$ and $121{cm}^2$. If $EF=15.4cm$, find $BC$.

• A. $11.2cm$
• B. $11.6cm$
• C. $11.4cm$
• D. $10.8cm$

Answer 1

Answer: (A)

$11.2cm$

$△ABC\sim △DEF$ (Given)
$\Rightarrow \frac{ar\left(ABC\right)}{ar\left(DEF\right)}=\frac{{BC}^2}{{EF}^2}$ (ratio of Areas of Similar triangles are equal to ratio of squares of corresponding sides)
$\Rightarrow \frac{64}{121}=\frac{{BC}^2}{{EF}^2}{\left\{\frac{BC}{EF}\right\}}^2={\left\{\frac{8}{11}\right\}}^2$
$\Rightarrow \frac{BC}{EF}=\frac{8}{11}\Rightarrow BC=\frac{8}{11}\times EF$
$\Rightarrow BC=\frac{8}{11}\times 15.4cm=11.2cm$