Question

Triangle ABC is right angled at B and the perpendicular drawn from B to the opposite side AC bisects it at D. If AD = DC = 5 cm, then BD =_______ .

Answer 1

If a perpendicular is drawn from the vertex of the right angle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to each other and to the whole triangle.
Here, $△ABC$ is right angled triangle at B and BD is the perpendicular drawn to the opposite side
$\therefore △ABD\sim △BCD$
$\Rightarrow$ $\frac{BD}{CD}=\frac{AD}{BD}$
$\Rightarrow$ ${BD}^2=AD\times DC$
$\Rightarrow$ ${BD}^2=5\times 5$
$\Rightarrow$ $BD=\sqrt{25}=5\text{cm}$