Question

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?

Answer 1

Answer:

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).