Question

Mid-points of the sides $AB$ and $AC$ of $△ABC$ are $(3,5)$ and $(-3,-3)$ respectively, then find the length of $BC$

Answer 1

$△\left(ADE\right)$ and $△\left(ABC\right)$

$\frac{AD}{AB}=\frac{AE}{AC}i<A$ common $DE||BC$

$\Rightarrow ADE\approx ABC\Rightarrow \frac{AD}{AB}=\frac{DE}{BC}=\frac{1}{2}\Rightarrow BC=2DE$

$\Rightarrow BC=2\sqrt{(3+3{)}^2+(5+3{)}^2}$

$=2\times 10=20$