Question

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

Short answer

The value of $x$ is $8\sqrt{2}$.

Step-by-step solution

Step 1. Given information.

The given figure is observed that a rectangle.

Step 2. Theorem used.

We use Pythagoras Theorem.

Pythagoras Theorem state 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.

The opposite sides of the rectangle are equal.

$\begin{array}{l}AB=8\\ DC=8\end{array}$

Calculation:

In $\Delta BDC$.

We use Pythagoras Theorem.

$\begin{array}{l}{x}^2=8^2+8^2\\ x^2=64+64\\ x^2=128\end{array}$

Taking square root we get.

$\begin{array}{l}x=\pm \sqrt{128}\\ x=\pm \sqrt{8\times 8\times 2}\\ x=\pm 8\sqrt{2}\end{array}$

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

Therefore, the value of $x$is $8\sqrt{2}$.