Question

In the given figure, find the length of BD.

• A. 2 cm
• B. 4 cm
• C. 6 cm
• D. 8 cm

Answer 1

The correct option is B 4 cm

Let $\angle A=x$
So, $\angle C={90}^{\circ }-x$
$ABD={90}^{\circ }-x$
$\angle CBD={90}^{\circ }-({90}^{\circ }-x)=x$

In $△ABD$ and $△BCD$,
$\angle A=\angle CBD$
$\angle C=\angle ABD$
$\angle ADB=\angle BDC$ (each ${90}^{\circ }$)

By AAA criteria
$△ABD\sim △BCD$
$B{D}^2=AD\times CD$
$B{D}^2=2cm\times 8cm$
$BD=4cm$