Chapter 16.3, Problem 1PS

To determine

To find: The value of $x$ in the given figure.

Answer to Problem 1PS

The value of $x$ in the given figureis $x=\frac{-11+\sqrt{181}}{2}$ .

Explanation of Solution

Given information:

The given figure is,

  

The value of $x$ in the given figureis calculated as by using Stewart’s Theorem,

  $\begin{array}{l}{\left(5\right)}^{2}x+{\left(8\right)}^2\left(3\right)={\left(7\right)}^2\left(3+x\right)+\left(3+x\right)\left(3x\right)\\ 25x+192=147+49x+9x+3x^2\\ x^2+11x-15=0\\ x=\frac{-11\pm \sqrt{{11}^2-4\left(1\right)\left(-15\right)}}{2\left(1\right)}\end{array}$

Simplify further,

  $x=\frac{-11+\sqrt{181}}{2}$

Thus, the value of $x$ in the given figure is $x=\frac{-11+\sqrt{181}}{2}$ .