Question

What are the limits between which the third side of the triangle lies, if the following are its two sides? 

4.8 cm, 6.4 cm

Answer 1

Triangle Inequality Theorem

For any triangle with sides a, b, c:

|a − b| < c < a + b

where c is the third side:

Given:

First side: = a = 4.8 cm

Second side: b = 6.4 cm

Step 1: Find lower limit

|a − b| = |6.4 − 4.8| = 1.6

So, c > 1.6

Step 2: Find upper limit

a + b = 6.4 + 4.8 = 11.2

So, c < 11.2

The third side of the triangle lies between 1.6 cm and 11.2 cm.

1.6 cm < x < 11.2 cm