Chapter 8.2, Problem 14CE

To determine

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

Answer to Problem 14CE

The required value of x is $x=\sqrt{52}$

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,

  $\begin{array}{l}{4}^2+6^2=x^2\\ 16+36=x^2\\ 52=x^2\end{array}$

Taking square root we get

  $x=\pm \sqrt{52}$

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

Therefore, the required value of x is $x=\sqrt{52}$