if the sides of given triangle are integers, how many different values can AC take
Answers
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.
Given:
Sides of given triangle are integers
To Find:
How many different values can AC take?
Solution:
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
Hence, this way, we have 4 distinct triangles following the above given 3 conditions.