The perimeter of an isosceles triangle is 28cm. AB =4ycm,AC=(6y-2x+1)cm and BC =(x+2y)cm. Find x and y, state the lengths of the triangle.

Answer 1

You know that the perimeter is 28, meaning

4y + 6y-2x+1 + x+2y = 28
x-12y = -27

Since the triangle is isosceles, you also need one of these equations:
4y = 6y-2x+1
4y = x+2y
6y-2x+1 = x+2y

So, just work your way through the possibilities, and you wind up with

(x,y) = (3,5/2)
(x,y) = (27/5,27/10)
(x,y) = (15/4,41/16)

Now, just check those solutions to see which one(s) produce values that qualify for sides of a triangle: No negative lengths, each side less than the sum of the other two.