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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
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