Question

Let two sides of triangle be 1 and 2004. If third side is also an integer,
then possible perimeter of triangle is
​

Answer 1

Given:

Two sides of a triangle are 1 and 2004 units.

Third side is also an integer.

To find:

Possible perimeter of triangle = ?

Solution:

Let us learn about the property of a triangle when two sides are given and the range of length of sides.

When the two sides of a triangle are given as 'a' and 'b', then the third side 'c' has a value which lies in the range:

$a-b<c<a+b$

Here, the two sides are 1 and 2004.

Let the third side be $x$.

As per the above condition:

$a-b = 2004 -1 =2003$

$a+b = 2004 +1 =2005$

The third side will be:

$2003<x<2005$

Given that third side is an integer so only value possible here is 2004.

So, the perimeter of triangle = Sum of length of all the sides

Perimeter = 1 + 2004 + 2004 = 4009