Question

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.

plzz solve this :)

Answer 1

Given : The length of the sides of a triangle are 2x + y/2 , 5x/3 + y + 1/2 and 2/3 x + 2y + 5/2  . triangle is equilateral.

To find : Perimeter of Triangle

Solution:

Equilateral triangle has all sides of equal length

hence

2x  + y/2  = 5x/3  + y  + 1/2   =   2x/3  + 2y  + 5/2

5x/3  + y  + 1/2   =   2x/3  + 2y  + 5/2

=> x   = y  + 2     Eq1

2x  + y/2  = 5x/3  + y  + 1/2

=> x/3   = y/2  +  1/2

=> 2x/3 =  y + 1      Eq2

Eq 1  - Eq2

=> x/3 = 1

=> x = 3

Substituting in Eq 1 or Eq 2

=> y = 1

2x  + y/2   = 13/2

5x/3  + y  + 1/2  = 13/2

2x/3  + 2y  + 5/2 = 13/2

Length of Each side = 13/2

Perimeter of triangle = 3 (13/2)  = 39/2

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Answer 2

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Given : The length of the sides of a triangle are 2x + y/2 , 5x/3 + y + 1/2 and 2/3 x + 2y + 5/2  . triangle is equilateral.

To find : Perimeter of Triangle

Solution:

Equilateral triangle has all sides of equal length

hence

2x  + y/2  = 5x/3  + y  + 1/2   =   2x/3  + 2y  + 5/2

5x/3  + y  + 1/2   =   2x/3  + 2y  + 5/2

=> x   = y  + 2     Eq1

2x  + y/2  = 5x/3  + y  + 1/2

=> x/3   = y/2  +  1/2

=> 2x/3 =  y + 1      Eq2

Eq 1  - Eq2

=> x/3 = 1

=> x = 3

Substituting in Eq 1 or Eq 2

=> y = 1

2x  + y/2   = 13/2

5x/3  + y  + 1/2  = 13/2

2x/3  + 2y  + 5/2 = 13/2

Length of Each side = 13/2

Perimeter of triangle = 3 (13/2)  = 39/2