Question

$\Delta ABC\sim \Delta DEF$ and their areas are respectively 64 $c{m}^2$ and 121 $c{m}^2$. If EF = 15.4 cm, find BC.

Answer 1

We have

$\Delta ABC\sim \Delta DEF$

$area\left(\Delta ABC\right)=64c{m}^2$

$area\left(\Delta DEF\right)=121c{m}^2$

$EF=15.4cm$

Since the ratio of the area of a triangle is equal to the square of the ratio of the sides.

So,

$\frac{area\left(\Delta ABC\right)}{area\left(\Delta DEF\right)}=(\frac{BC}{EF}{)}^2$

$(\frac{BC}{EF}{)}^2=\frac{64}{121}$

$\frac{BC}{EF}=\frac{8}{11}$

$\frac{BC}{15.4}=\frac{8}{11}$

$BC=\frac{8}{11}\times 15.4=11.2cm$