Question

What is the length of AD in the given figure?

• A. $2\sqrt{3}$ m
• B. $\sqrt{3}$ m
• C. $\sqrt{8}$ m
• D. $\sqrt{12}$ m

Answer 1

Answer: (A), (D)

The correct options are
A

$2\sqrt{3}$ m

D

$\sqrt{12}$ m

In the given figure ABC is a right-angled isosceles triangle

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

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

Here $x=2$ m

$\therefore AC=\sqrt{2}x$ $=$ $2\sqrt{2}$ m

Now, in $△$ $ACD$,

$AC$ = $2\sqrt{2}$ m and $CD=2$ m

Using Pythagoras theorem,

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

AD = $\sqrt{(2\sqrt{2}{)}^2+2^2}$

= $\sqrt{8+4}$

= $\sqrt{12}$

= $2\sqrt{3}$ m