Chapter 16.3, Problem 2PS

To determine

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

Answer to Problem 2PS

The value of $y$ in the given figureis $\frac{\sqrt{31}}{2}\text{unit}$ .

Explanation of Solution

Given information:

The given figure is,

  

The value of $y$ in the given figure is calculated as by using Stewart’s Theorem,

  $\begin{array}{l}{\left(3\right)}^2\left(3\right)+{\left(4\right)}^2\left(1\right)={\left(y\right)}^2\left(4\right)+4\left(1\right)\left(3\right)\\ 27+16=4y^2+12\\ y^2=\frac{31}{4}\\ y=\frac{\sqrt{31}}{2}\text{unit}\end{array}$

Thus, the value of $y$ in the given figure is $\frac{\sqrt{31}}{2}\text{unit}$ .