Question

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 ?

Answer 1

2a +2b +4

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.