A triangle has a perimeter of 10a + 3b + 12 and has sides of length 3a + 8 and 5a + b what is the length of the third side?

2a + 2b + 4

Step-by-step explanation:

The perimeter is the sum of the lengths of the three sides. If x represents the length of the third side, then ...

(3a + 8) + (5a + b) + x = (10a + 3b + 12)

Subtracting from the equation everything on the left side that is not x, we get ...

x = (10a + 3b + 12) - (3a + 8) - (5a + b)

= a (10 - 3 - 5) + b (3 - 1) + (12 - 8)

= 2a + 2b + 4

The length of the third side is 2a + 2b + 4.