Question

In the given figure, AB equal to ___ units.

• A. $\sqrt{2}$
• B. $3\sqrt{2}$
• C. $2\sqrt{2}$
• D. $4\sqrt{2}$

Answer 1

The correct option is D

$4\sqrt{2}$

$\text{Using Pythagoras' theorem in right-angled triangle ABD,}A{B}^2=A{D}^2+B{D}^2.---\left(i\right)\text{Using it in}△ADC,\text{we get}A{C}^2=A{D}^2+D{C}^2.\Rightarrow A{D}^2=A{C}^2-D{C}^2=4^2-3^2=16-9=7$
Substituting this value of $A{D}^2$ in (i), we get
$A{B}^2=7+5^2=7+25=32.$
$\Rightarrow AB=\sqrt{32}=4\sqrt{2}$ units