Chapter 8.2, Problem 13CE

To determine

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

Answer to Problem 13CE

The required value of x is $x=\sqrt{51}$

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,

  $\begin{array}{c}{x}^2+7^2={10}^2\\ x^2={10}^2-7^2\\ =100-49\\ =51\end{array}$

Taking square root we get

  $x=\pm \sqrt{51}$

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

Therefore, the required value of x is $x=\sqrt{51}$