Question

∆ABC is an equlateral traingle in which AB=(3x+1)cm, BC=(2x+3y+5)cm and AC=(x+9y+6)cm. find the value of x and y

Answer 1

AB = BC = AC

AB = BC
3x + 1 = 2x + 3y + 5 
3x - 2x - 3y = 5 - 1 
x - 3 y = 4 → 1 

BC = AC
2x + 3y + 5 = x + 9y + 6 
2x + 3y - x - 9y = 6 - 5
x - 6y = 1 → 2

Subtracting 1 from 2
x - 6y - x + 3y = 1 - 4 = -3 
-3y = -3 
y = 1 

Substituting y = 1 in 1 
x = 7
Side = 22 cm

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Answer 2

Here is your answer.
In the picture.