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

The third side of the triangle is (7a + 2b - 1).

Step-by-step explanation:

The length of the first side = (3a + 8)

The length of the second side = (5 + b)

Let us assume the third side = m

The perimeter of the triangle = SUM OF ALL 3 SIDES

⇒ (10a + 3b + 12) = (3a + 8) + (5 + b) + m

or, (10a + 3b + 12) = 3a + b + 13 + m

or, m = (10a + 3b + 12) - (3a + b + 13)

= 10 a + 3b + 12 - 3a - b - 13

= 7a + 2b - 1 = (10 - 3a) + (3b - b) + 12 - 13

or, m = (7a + 2b - 1)

Hence, the third side of the triangle is (7a + 2b - 1).