Page 2 - ln1

Sum of the lengths of two sides of a triangle

The sum of the lengths of any two sides of a triangle is greater than the third side.

In the above triangle,
9+11=20 >14
11+14=25 >9
9+14=23 >11

Example:-

Is it possible to have a triangle with the following sides?

3 cm, 6 cm, 7 cm

Given that, the sides of the triangle are 3 cm, 6 cm, 7 cm.

Here, 3 + 6 =9 cm > 7 cm
6 + 7 = 13 cm > 3 cm
3 + 7 = 10 cm > 6 cm
hence, this triangle is possible

Example:
ABCD is a quadrilateral.
Is AB + BC + CD + DA > AC + BD?

Solution
Considering DABC,
AB + BC > CA (i)
In DBCD,
BC + CD > DB (ii)
In DCDA,
CD + DA > AC (iii)