Question

The areas of two similar triangles $\Delta ABC$ and $\Delta DEF are $36$ ${cm}^{2}and81{cm}^2$ respectively. If EF =6.9cm, find BC

Answer 1

Since the triangles are similar .

$\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta DEF\right)}={\left(\frac{BC}{EF}\right)}^2\Rightarrow \frac{36}{81}={\left(\frac{BC}{6.9}\right)}^2\Rightarrow \frac{6}{9}=\frac{BC}{6.9}\Rightarrow BC=\frac{6}{9}\times 6.9\Rightarrow BC=4.6cm$