Question

Find the perimeter of triangle whose two sides are of length $12\sqrt{2}$ m each. The length of the third side is equal to the length of diagonal of square of side $10$m ?

• A. $34$ m
• B. $34\sqrt{2}$ m
• C. $44$ m
• D. Cannot be determined.

Answer 1

The correct option is B $34\sqrt{2}$ m

Let, the diagonal of square be $x$.


Now, applying pythagoras theorem,
$x={10}^2+{10}^2$
$x=\sqrt{100+100}$
$x=\sqrt{200}$
$x=10\sqrt{2}$m
Now, a triangle having one side as $10\sqrt{2}$ m and two sides as $12\sqrt{2}$ m each will have perimeter as,
Perimeter $=12\sqrt{2}+12\sqrt{2}+10\sqrt{2}$
Perimeter $=34\sqrt{2}$ m

Hence, option$\left(b\right)$ correct.