Atriangle has a perimeter of 10x+2. two sides have lengths of 5x and 2x+9. what is the length of the 3rd side?

As we know perimeter of triangle is equal to sum of all three sides.

Let the third side = a.

So we can write perimeter as = 5x + 2x + 9 + a

As given perimeter = 10x + 2

So we can write 10x +  2 = 7x + 9 + a

10x + 2 - 7x - 9 = a

3x - 7 = a

So third side = 3x - 7.