Question

In a triangle if two sides are 13 and 19, then find the number of possible triangles. Whose

sides are integral values?​

Answer 1

Answer:

TO FIND THE NUMBER OF DISTINCT TRIANGLES, with integer sides & perimeter 14…

Following points are to be considered…

(1): All side lengths have integral values ie we can only start from 1 onwards…

(2): side1 + side2 + side3 = 14

(3): The sum of 2 sides of a triangle is greater than the third side.

Taking the above points into consideration…

None of the sides can be 1 & none of the sides can be either of 7,8,9,10,11,12,13,&14…

So we have , only options left..

2+6+6 = 14

3+5+6 = 14

4+4+6 = 14

4+5+5 = 14

So, this way, we have 4 distinct triangles following the above given 3 conditions.