Question

What is the Length of the side AD in the given figure?

• A. $2\sqrt{2}$ m
• B. $2\sqrt{5}$ m
• C. $\sqrt{5}$ m
• D. $\sqrt{3}$ m

Answer 1

The correct option is C

$\sqrt{5}$ m

ABC is a right - angled isosceles triangle.

The sides are in the ratio 1 : 1 : $\sqrt{2}$

Let the sides be x , x , $\sqrt{2}$ x

Here x = $\sqrt{2}$

$\therefore$ The Length of AC = $\sqrt{2}$ x = $\sqrt{2}\times \sqrt{2}$ = 2 m

Hence, using Pythagoras theorem we can say :

AD = $\sqrt{C{D}^2+A{C}^2}$

$\sqrt{1^2+2^2}$ = $\sqrt{5}$ m