Question

Triangles $ABC$ and $DEF$ are similar. If their areas are $100c{m}^2$ and $49c{m}^2$ respectively and $BC$ is $8.2cm$ then $EF=$

• A. $5.47cm$
• B. $5.74cm$
• C. $6.47cm$
• D. $6.74cm$

Answer 1

The correct option is B $5.74cm$

Given: Area of similar triangles $100{cm}^2$ and $49{cm}^2$

$BC=8.2cm$

Let ,$EF=x$

For similar triangle,

${\text{Ratio of corresponding sides}}^2=\text{Ratio of their Area}$

$\therefore$ $\frac{{8.2}^2}{x^2}=\frac{100}{49}$

$\frac{67.24}{x^2}=\frac{100}{49}$

$100x^2=67.24\times 49$

$x^2=\frac{67.24\times 49}{100}$

$x^2=32.9476$

$x=5.74cm$

$\Rightarrow EF=5.74cm$