Question

$△$ ABC is a right angled triangle, right angled at B and the perpendicular drawn from B to the opposite side bisects it at D. BD = ___ cm, if AD = DC = 5 cm.

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.
Here, $△$ ABC is right angled triangle at B and BD is the perpendicular drawn to the opposite side
Therefore, $△ABD\sim △BCD$
$\Rightarrow$ $\frac{BD}{CD}=\frac{AD}{BD}$
$\Rightarrow$ ${BD}^2=AD\times DC$
$\Rightarrow$ ${BD}^2=5\times 5$
$\Rightarrow$ $BD=\sqrt{25}=5\text{cm}$