Question

In $\Delta ABD,AB\perp BD$ and $AC=BD$. If $AB=4cm,BC=2cm$. find $AD$

• A. $6cm$
• B. $4cm$
• C. $7cm$
• D. $3cm$

Answer 1

The correct option is A $6cm$

Given $AC=BD$ $AB=4cm$, $BC=2cm$

Applying Pythagoras in $△ABC$

$A{C}^2=A{B}^2+B{C}^2$

$A{C}^2=4^2+2^2$

$AC=\sqrt{16+4}$

$AC=\sqrt{20}$

$AC=2\sqrt{5}cm$

Since $AC=BD=2\sqrt{5}$

Now applying Pythagoras in $△ABD$

$A{D}^2=A{B}^2+B{D}^2$

$A{D}^2=4^2+(2\sqrt{5}{)}^2$

$AD=\sqrt{16+20}$

$AD=\sqrt{36}$

$AD=6cm$