Question

The sides (in cms) of an equilateral triangle are $2x-3y+1,x+y-1$, and ($3x-y-9$). Find its perimeter

Answer 1

As all the sides of an equilateral triangle are equal, $2x-3y+1=x+y-1$ and $x+y-1=3x-y-9$. Hence
$x-4y=-2,........\left(1\right)$
$2x-2y=8...........\left(2\right)$
Multiplying $\left(2\right)$ by $2$ and subtracting $\left(1\right)$ from it, we get $3x=18$. Hence $x=6$.
Finally $2y=2x-8=2\left(6\right)-8=12-8=4$. Hence $y=2$.
Thus the side of the triangle is $x+y-1=6+2-1=7cm$. Its perimeter is $3\times 7=21cm$.