The perimeter of an isosceles triangle is 7x+5y-8 units and the length of the base of the triangle is x-y-2 units. What is the length, in units, of each of the congruent sides of the triangle?

3x + 3y - 3 units each

Step-by-step explanation:

An isosceles triangle is one that has two equal sides and angles.

given: perimeter = 7x + 5y - 8 units

          base length = x - y -2 units

The length of each congruent sides can be determined as follows:

Let the length of the sides be represented by t. Since the sides have equal length, then;

7x + 5y - 8 = t + t + (x - y -2)

7x + 5y - 8 = 2t + (x - y -2)

⇒ 2t = 7x + 5y - 8 - (x - y -2)

       = 7x + 5y - 8 - x + y + 2

collecting like terms,

2t  = 6x + 6y - 6

    = 2(3x + 3y - 3)

divide both sides by 2,

t = 3x + 3y - 3

Therefore, the congruent sides are 3x + 3y - 3 units each.