Chapter 8.2, Problem 7WE

To determine

To Find: Find the value of x from the given figure.

Answer to Problem 7WE

The required value of x is $x=4\sqrt{2}$

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,

  $\begin{array}{c}{x}^2+4^2={\left(4\sqrt{3}\right)}^2\\ x^2+16=48\\ x^2=48-16\\ =32\end{array}$

Taking square root we get

  $\begin{array}{c}x=\pm \sqrt{32}\\ =\pm 4\sqrt{2}\end{array}$

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

Therefore, the required value of x is $x=4\sqrt{2}$