Chapter 4.4, Problem 27WE

To determine

Value of x and y.

Answer to Problem 27WE

Value of $x=1\text{and}y=-3$

Explanation of Solution

Given:

For an equilateral triangle $\Delta ABC$

  $AB=4x-y,BC=2x+3y\text{and }AC=7$

As the $\Delta ABC$ is an equilateral triangle.

So the sides $AB=BC=AC$

So, taking

  $\begin{array}{l}AB=AC\\ \Rightarrow 4x-y=7\\ \Rightarrow y=4x-7\mathrm{......}\left(1\right)\end{array}$

And taking

  $\begin{array}{l}BC=AC\\ \Rightarrow 2x+3y=7\mathrm{.......}\left(2\right)\end{array}$

Substituting the value of y in (2)

  $\begin{array}{l}2x=7-3\left(4x-7\right)\\ \Rightarrow 14x=14\\ \Rightarrow x=1\end{array}$

And substituting the value of x in (1)

  $\begin{array}{l}y=4\left(1\right)-7\\ \Rightarrow y=-3\end{array}$

Therefore, $x=1\text{and}y=-3$