Chapter 16, Problem 1RP

To determine

To find: The value of $x$ and $y$ .

Answer to Problem 1RP

The value of $x$ and $y$ are $\frac{\sqrt{165}}{3}$ and $\sqrt{93}$ respectively.

Explanation of Solution

Given information:

The given figure is,

  

The given figure is,

  

Obtain the equation in term of $x$ and $y$ , by using Stewart’s theorem as,

  $\begin{array}{l}3x^2+4y^2=343+43\\ 3x^2+4y^2=427\end{array}$ …… (1)

The given figure is,

  

Obtain the equation in term of $x$ and $y$ , by using Stewart’s theorem as,

  $\begin{array}{l}6x^2+2y^2=200+96\\ 3x^2+4y^2=148\end{array}$ …… (2)

From equation (1) and (2),

  $\begin{array}{l}x=\frac{\sqrt{165}}{3}\\ y=\sqrt{93}\end{array}$

Thus, the value of $x$ and $y$ are $\frac{\sqrt{165}}{3}$ and $\sqrt{93}$ respectively.