if two sides of triangle are 15 and 25 cm respectively,what is the range of values of the third side?

10 to 40 cm.

(minimum = difference ; maximum = sum)

It is sometimes called the 'triangle rule'

http://www.freemathhelp.com/feliz-triangle-inequalities.html

To find the range of values for the third side of a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

The given information states that two sides of the triangle have lengths 15 cm and 25 cm. Let's denote these sides as a = 15 cm and b = 25 cm. Now, we can use the triangle inequality theorem to find the range of values for the third side, which we'll call c.

The triangle inequality theorem can be written as:

a + b > c

Substituting the given values:

15 cm + 25 cm > c

40 cm > c

Therefore, the third side (c) must be less than 40 cm in order to form a valid triangle.

To find the lower bound of the range of values for c, we can use the absolute difference between the two given sides:

|a - b| < c

Substituting the given values:

|15 cm - 25 cm| < c

|-10 cm| < c

10 cm < c

Therefore, the third side (c) must be greater than 10 cm to form a valid triangle.

In conclusion, the range of values for the third side (c) of the triangle is greater than 10 cm and less than 40 cm, i.e., 10 cm < c < 40 cm.