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Triangles and their Properties

A triangle is a figure enclosed by three sides. In the figure given below ABC is a triangle with sides AB, BC and CA measuring c, a and b units respectively. Line AD represents the height of the triangle corresponding to the side BC and is denoted by h.
 
Description: P-321-3.tif
 
In any triangle ABC
Area Description: 7382.png× BC × AD Description: 7375.png a × h

Properties of a Triangle

  • The sum of all the angles of a triangle = 180°
  • The sum of lengths of the two sides > Length of the third side
  • The difference of any two sides of any triangle < length of the third side
  • The area of any triangle can be found by several methods:
    1. Area of any triangle Description: 7367.png × base × perpendicular to base from the opposite vertex.
    2. Area of any triangle Description: 7360.png where S is the semi-perimeter of the triangle and a, b and c are the sides of a triangle.
    3. Area of any triangle Description: 7353.png× bc Sin A
Besides, there are some formulae which we use ex­clusively in some particular cases.

 
Example
What is the number of distinct triangles with integral valued sides and perimeter as 14?
  1. 6
  2. 5
  3. 4
  4. 3
Solution
The sum of the lengths of the two sides > the length of the third side
 
So, the maximum length of any particular side can be 6 units.
 
Now if a = 6, then b + c = 8, so the possible sets are
(6, 6, 2), (6, 5, 3) and (6, 4, 4)
If a = 5, then b + c = 9, so the possible set is (5, 5, 4)
 
So, the number of distinct triangles = 4
 





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