Question

In the given figure, the length of side AB is :

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

Answer 1

The correct option is C

$4\sqrt{2}units$

$\text{In right angle triangle ABD}A{B}^2=A{D}^2+B{D}^2...\left(i\right)\text{In}ADCA{C}^2=A{D}^2+D{C}^{2}A{D}^2=A{C}^2-D{C}^2...\left(ii\right)\text{Substituting the value of AD from (ii) in eq (i)}A{B}^2=A{C}^2-D{C}^2+B{D}^2\text{Substituting the values, we get,}A{B}^2=4^2-3^2+5^{2}A{B}^2=16-9+25=32$
$\Rightarrow AB=\sqrt{32}=4\sqrt{2}units$.