Question

Find the values of$\mathit{x}$ and y.

27. ln equiangular $\mathit{\Delta }\mathbf{ABC}$,$\mathbf{AB}\mathbf{=}\mathbf{4}\mathbf{x}\mathbf{-}\mathbf{y}\mathbf{,}\mathbf{BC}\mathbf{=}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{3}\mathbf{y}$ and $\mathbf{AC}\mathbf{=}\mathbf{7}$.

Short answer

The value of$x$ and$y$ is 2and 1 respectively.

Step-by-step solution

– Apply definition of equilateral triangle.

An equilateral triangle is a triangle which all the three sides are equal in length.

Therefore, in $\Delta ABC,AB=BC=AC$.

– Description of step.

Consider, $AB=AC$.

Substitute $4x-y$for 7 and for $AC$into $AB=AC$and simplify.

$\begin{array}{l}4x-y=7\\ y=4x-7\end{array}$

– Description of step.

Consider, $BC=AC$.

Substitute 7 for $AC$and $2x+3y$for $BC$into $BC=AC$and simplify.

$2x+3y=7$

– Description of step.

Substitute$4x-7$ for$y$ into $2x+3y=7$, to find the value of $x$.

$\begin{array}{l}2x+3(4x-7)=7\\ 2x+12x-21=7\\ 14x=28\\ x=2\end{array}$

– Description of step.

Substitute 2 for$x$ into $y=4x-7$, to find the value of $y$.

$\begin{array}{l}y=4\times 2-7\\ =8-7\\ =1\end{array}$

Therefore, the value of$x$ and$y$ is 2 and 1 respectively.