Question

Question 1
Let $\Delta ABC\sim \Delta DEF$ and their areas be, respectively, $64c{m}^2$ and $121c{m}^2$. If EF = 15.4 cm, find BC.

Answer 1

It is given that,
Area of $\Delta ABC=64c{m}^2$
Area of $\Delta DEF=121c{m}^2$
EF = 15.4 cm
in, $\Delta ABCand\Delta DEF$
$\therefore \frac{Areaof\Delta ABC}{Areaof\Delta DEF}=\frac{A{B}^2}{D{E}^2}=\frac{A{C}^2}{D{F}^2}=\frac{B{C}^2}{E{F}^2}...\left(i\right)$
[If two triangles are similar, ratio of their areas are equal to the square of the ratio of their corresponding sides.]
$\therefore \frac{64}{121}=\frac{B{C}^2}{E{F}^2}$
$\Rightarrow (\frac{8}{11}{)}^2=(\frac{BC}{15.4}{)}^2$
$\Rightarrow \frac{8}{11}=\frac{BC}{15.4}$
$\Rightarrow BC=\frac{8\times 15.4}{11}=11.2cm$