Two sides of a triangle are 10 cm and 15 cm.
What is the range of possible lengths for the
third side?
Write inequality?
well, any two sides have to be longer than the other side.
10+s>15 and
10+15>s
25>s>5
To find the range of possible lengths for the third side of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's denote the length of the third side as "x". According to the triangle inequality theorem, we can write the following inequality:
10 + 15 > x
25 > x
This inequality states that the sum of the lengths of the two given sides (10 cm and 15 cm) must be greater than the length of the third side (x). By simplifying, we find that x must be less than 25 cm.
Therefore, the range of possible lengths for the third side is x < 25 cm.