Question

the perimeter of an isosceles triangle is 28, the sides are 4b, 6b-2a+1 and a+2b respectively. find the values of a and b hence state the lenghts of the sides of the triangle

Answer 1

since two sides are equal, you must have one of

4b=6b-2a+1
4b=a+2b
6b-2a+1=a+2b
which can be simplified to
2b-2a = -1
a-2b = 0
3a-4b = 1

also, using the perimeter,

4b + 6b-2a+1 + a+2b = 28
12b-a=27

so, see how the perimeter equation can be matched with one of the others to produce results that are valid as sides of a triangle.