Chapter 8.2, Problem 16CE

To determine

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

Answer to Problem 16CE

The required value of x is $x=\sqrt{117}$

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,

  $\begin{array}{c}{6}^2+9^2=x^2\\ 36+81=x^2\\ 117=x^2\end{array}$

Taking square root we get

  $x=\pm \sqrt{117}$

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

Therefore, the required value of x is $x=\sqrt{117}$