Question

Find the perimeter of a triangular park whose two sides are of length $12\sqrt{2}$meters each. The length of the third side is equal to the length of the diagonal of the square of a side that measures $10$ meters.

• A. $44m$
• B. $44\sqrt{2}m$
• C. $34m$
• D. $34\sqrt{2}m$

Answer 1

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

Let the diagonal of the square be $x.$

Applying the Pythagorean theorem,
$x^2={10}^2+{10}^2$
$\Rightarrow x=\sqrt{100+100}$
$\Rightarrow x=\sqrt{200}$
$\Rightarrow x=\sqrt{2\times 10\times 10}$
$\Rightarrow x=10\sqrt{2}m$
Now, a triangle having one side of $10\sqrt{2}m$ and two sides of $12\sqrt{2}m$ each will have:
Perimeter $=12\sqrt{2}+12\sqrt{2}+10\sqrt{2}$
$\Rightarrow$ Perimeter $=34\sqrt{2}m$