In triangle ABC length a=5 & b=6. C is an integer. What's the largest possible perimeter of the triangle?

Answer 1

Any 3rd side of a triangle cannot exceed the sum of the other two sides' measurements. So C cannot exceed 11 (=5+6), and, in fact, cannot actually be 11 either as there isn't much of a triangle (it would require the angle between A and B to be 180 degrees, and the other two angles to be 0 degrees).

The largest possible perimeter, given a and b, would be when C is the largest possible value. It cannot equal 11, and must be an integer, so the next highest integer is the largest C can be. So C must equal 10 when the perimeter is the largest possible.

That makes the largest possible perimeter 21 (=5+6+10).

Answer 2

c has to be less than a+b, otherwise you don't have a triangle. Since c is an integer, the possible value of c is 10, and the largest possible perimeter of the triangle is 21.

Answer 3

1

Answer 4

c<5+6
5 6 c=10
P=5+6+10=21

21

To find this, you must find the third side that is less than 5+6. Then, add all sides and you get 21.