the perimeter of a triangle is 8x+3y. The length of two sides of the triangle are 4x+y and 2x-3y. Find the measure of the third side of the triangle.

Perimeter = Sum of three sides.

Let the third side be = t

Perimeter = 8x + 3y

8x + 3y = (4x + y) + (2x - 3y) + t

8x + 3y = 4x + y + 2x - 3y + t

8x + 3y = 4x + 2x + y - 3y + t

8x + 3y = 6x - 2y + t

8x - 6x + 3y + 2y = t

2x + 5y = t.

Therefore third side = 2x + 5y