Chapter 8.2, Problem 17CE

To determine

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

Answer to Problem 17CE

The required value of x is $x=\sqrt{7}$

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,

  $\begin{array}{l}{x}^2+x^2={\left(7\sqrt{2}\right)}^2\\ 2x^2=49\times 2\\ x^2=49\end{array}$

Taking square root we get

  $\begin{array}{c}x=\pm \sqrt{49}\\ =\pm 7\end{array}$

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

Therefore, the required value of x is $x=\sqrt{7}$