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In DDAB,
DA + AB > DB (iv)
Adding equations (I), (//), (iii), and (iv), we obtain
AB + BC + BC + CD + CD + DA + DA + AB > AC + BD + AC + BD
2AB + 2BC + 2CD +2DA > 2AC + 2BD
AB + BC + CD + DA > AC + BD

Difference between lengths of two sides of a triangle

The difference between lengths of any two sides is smaller than the length of the third side.

 In the above triangle,
11 – 9 = 2 < 14
14 – 11 = 3 < 9
14 – 9 = 5 < 11

Using the concept of sum of two sides and difference of two sides, it is possible to determine the
range of lengths that the third side can take.

Example: The lengths of two sides of a triangle are 12 cm and 15 cm. between what two
measures should the length of the third side fall?
Solution:-
There are two things for the triangle
(i) sum of the lengths of any two sides of a triangle is greater than the length of the third side.
(ii) Difference between the lengths of any two sides of a triangle is smaller than the length of the
third side.
Let x be the third side
so, from first point
12+15 > x
or x < 27 cm
Now from second point
15-12 < x
or x > 3
So x lies between 3 cm and 27 cm.