Chapter 8.2, Problem 18CE

To determine

To Find: Find the value of x in simplest radical form.

Answer to Problem 18CE

The required value of x is $x=5$

Explanation of Solution

Given information: We have given a figure as shown below

  

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,

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

Taking square root we get

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

Since square root is a positive quantity so we neglect negative sign.

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