Question

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

Short answer

The value of $x$ is $8$.

Step-by-step solution

Step 1. Given information.

The two sides are given $6$ and $10$.

Step 2. Theorem used.

We use Pythagorean Theorem.

Pythagorean 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:

$\begin{array}{c}{6}^2+x^2={10}^2\\ 36+x^2=100\\ x^2=64\end{array}$

Taking square root we get.

$\begin{array}{l}x=\pm \sqrt{64}\\ x=\pm 8\end{array}$

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

Therefore, the value of $x$is $8$.