Question

the length of 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 it's perimeter is. I will mark u as brainliest​

Answer 1

Answer:

For an Equilateral triangle, all three sides are equal in length.

==> 2x + y/2 = (5x/3) + y + 1/2 = (2/3)x + 2y + (5/2)

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

(or)

12x + 3y = 10x + 6y + 3

==> 2x - 3y = 3    --------- (1)

Also,

2x + (y/2) = (2/3)x + 2y + (5/2)

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

==> 12x + 3y = 4x + 12y + 15

==> 8x - 9y = 15    ---- (2)

Multiply (1) by 3 and solve it with (2).

6x - 9y - 8x + 9y = 9 - 15

==> -2x = -6

==> x = 3

Place x = 3 in (2).

==> 8x - 9y = 15

==> 24 - 9y = 15

==> -9y = 15 - 24

==> -9y = -9

==> y = 1

Place x and y values in the any equation.

2x + y/2

==> 6 + 1/2

==> 6.5

Perimeter = Side * 3

==> 6.5 * 3

==> 19.5 cm

Hence, Perimeter of equilateral triangle = 19.5 cm

Answer 2

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

Learn more:

https://brainly.in/question/1271372

Find the perimeter of a triangle whose sides are x+ 3y, 2x + y, x - y ...

https://brainly.in/question/11599325

perimeters of two similar triangles are 30cm and 40cm respectively ...

https://brainly.in/question/18128501