Question

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

• A. 23 cm
• B. 30 cm
• C. 21 cm
• D. 12 cm

Answer 1

The correct option is C 21 cm

As all the sides of equilateral triangle are equal,
2x - 3y + 1 = x + y - 1 - - - (1)
x + y - 1 = 3x - y - 9 - - - (2)
From equation (1), we have:
x - 4y + 2 = 0 - - - (3)
From equation (2), we have:
2x - 2y - 8 = 0 - - - (4)
Multiplying equation (4) by 2, we get
4x - 4y - 16 = 0 - - - (5)
Subtracting equation (5) from equation (3), we get:
-3x + 18 = 0
$\Rightarrow$ 3x = 18
$\therefore x=\frac{18}{3}=6$
Putting x = 6 in (3), we have:
6 - 4y + 2 = 0
$\Rightarrow$ 4y = 8
$\therefore y=\frac{8}{4}=2$
The perimeter of the equilateral triangle = 3 $\times$ length of one side
= 3(2x - 3y + 1) = 3[2(6) - 3(2) + 1] = 3 $\times$ 7 = 21
Therefore, the required perimeter = 21 cm