Question

In the given figure, $\angle$ ABC = 90 and BD $\perp$ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

Answer 1

Given:

$\angle BDC={90}^{\circ }$

$\angle ABC={90}^{\circ }$

Let $\angle BCD=x^{\circ }$

Using triangle sum property in $△BDC$, $\angle DBC=90-x^{\circ }$

Also $\angle ABD=x^{\circ }$

Using triangle sum property in $△ADB$, $\angle BAD=90-x^{\circ }$

Now considering $△BDC$ and $△ADB$

$\angle BDC=\angle BDA$

$\angle BCD=\angle ABD$

$\angle DBC=\angle DAB$

So by AAA

$△BDC\sim △ADB$

Hence $\frac{BC}{CD}=\frac{AB}{BD}$

$\frac{BC}{5.4}=\frac{5.7}{3.8}$

$BC=8.1$

Hence $BC=8.1cm$