Question

The sides of an equilateral triangle are given by $x+3y$; $3x+2y-2$ and $4x+\frac{1}{2}y+1$ respectively. Find the lengths of the sides of the triangle.

• A. $15$ units each
• B. $17$ units each
• C. $12$ units each
• D. $11$ units each

Answer 1

The correct option is A $15$ units each

Since it is an equilateral triangle, the lengths of the sides are equal

So, $x+3y=3x+2y-2=4x+\frac{1}{2}y+1$

$\therefore x+3y=3x+2y-2\therefore y=2x-2$

$2x-y=2$ ...(1)

Also, $4x+\frac{1}{2}y+1=x+3y$

$\therefore 8x+y+2=2x+6y6x+2=5y$

$6x-5y=-2$ ...(2)

Multiplying eq(1) by 5 we get,

$10x-5y=10$ ...(3)

Subtracting eq(2) from eq(3) we get,

$4x=12\Rightarrow x=3$

$\therefore y=2x-2=4$

The length of one side of equilateral triangle = $x+3y$ =$3+3\left(4\right)=15$units