Question

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

Short answer

The value of $x$ is $4\sqrt{5}$.

Step-by-step solution

Step 1. Given information.

The two sides are given 8 and 20.

Step 2. Theorem used.

We use Pythagoras Theorem.

Pythagoras Theorem define 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.

Simplify and do the calculation.

$\begin{array}{c}{8}^2+x^2={12}^2\\ 64+x^2=144\\ x^2=80\end{array}$

Taking square root we get.

$\begin{array}{l}x=\pm \sqrt{80}\\ x=\pm 4\sqrt{5}\end{array}$

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

Therefore, the value of $x$is $4\sqrt{5}$.