Question

Find the value of $x$ from the given figure.

Short answer

The value of $x$ is $6$.

Step-by-step solution

Step 1. Given information.

We have two sides $6$ and $6\sqrt{2}$.

Step 2. Theorem used.

We use Pythagoras Theorem.

Pythagoras Theorem states that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

Step 3. Now find the value.

Calculation:

$\begin{array}{c}{x}^2+6^2={\left(6\sqrt{2}\right)}^2\\ x^2+36=72\\ x^2=36°\end{array}$

Taking square root we get.

$\begin{array}{c}x=\pm \sqrt{36}\\ =\pm 6\end{array}$

Since, distance is a positive quantity. So, we neglect negative sign.

Therefore, the value of $x$is $6$.