Question

State an equation you could use to find the value of $x$. Then find the value of $x$ in simplest radical form.

Short answer

The required value of $x$ is,

$x=5$.

Step-by-step solution

Step 1. Given information.

We have given a figure as shown below,

Step 2. Use Pythagorean Theorem concept.

From Pythagorean Theorem,

we know that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

The given triangle is right triangle.

Therefore,

$\begin{array}{l}{x}^2+{\left(5\sqrt{3}\right)}^2={\left(2x\right)}^2\\ x^2+25\times 3=4x^2\\ 75=4x^2-x^2\\ 75=3x^2\\ 25=x^2\end{array}$

Step 3. Taking square root. 

we get,

$\begin{array}{c}x=\pm \sqrt{25}\\ =\pm 5\end{array}$

Step 4. Neglect negative sign.

Since, square root is positive quantity

So, we neglect negative sign.

Therefore, the required value of $x$ is, $x=5$.