Question

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

• A. 5 cm
• B. 6 cm
• C. 4.75 cm
• D. 5.2 cm

Answer 1

The correct option is A 5 cm

Since $△$ ABC is right angled triangle at B and BD is the perpendicular drawn to the opposite side,
Perpendicular from right angle to hypotenuse divides the triangle into two similar triangles and these are similar to the whole triangle also.

$△BDA\sim △CDB$
$\frac{BD}{DC}=\frac{BD}{AD}$
${BD}^2=AD\times DC$
$⟹{BD}^2=5\times 5$
$BD=\sqrt{25}=5\text{cm}$