The length of the sides of a triangle are 2x + y/2 , 5x/3 + y + 1/2  and 2/3 x  + 2y + 5/2. If the triangle is equilateral. Find its perimeter.

Ans: 2x + y/2

= 4x + y/2           ---------(1)

= 10x + 6y + 3 /6        ---------(2)

2/3 x + 2y + 5/2

= 4x + 12y+ 15 /6        ---------(3)

APQ:

(4x+ y)/2 = (10x + 6y + 3) /6  = (4x + 12y + 15) /6

24x + 6y= 20x + 12y + 6

4x + y/2 = 4x+ 12y + 15 /6

2x - 3y = 3         ---------(4)

24x + 6y = 8x + 24y + 30

Solve it, Solve it ,

To get 8x - 9y = 15 -----------(5) To get x = 3

Substitute value of x in (4)

2x- 3y = 3

Solve it ,

To get y = 1

So the values of x = 3 and y = 1

2x +y/2 = 6.5 cm

Perimeter = 6.5 cm + 6.5 cm + 6.5 cm

Perimeter = 19. 5cm

∴ the perimeter of the triangle is 19.5 cm