if two sides of a scalene triangle measure 10 and 12 the length of the third side could be?
Study similar post:
http://www.jiskha.com/display.cgi?id=1296822526
To determine the possible length of the third side of a scalene triangle, we can use the triangle inequality theorem. According to the theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's denote the lengths of the two sides measuring 10 and 12 as a and b, respectively. The length of the third side (c) can vary depending on the relationship between a, b, and c.
Using the triangle inequality theorem, we can write two inequalities:
a + b > c
b + c > a
Substituting the given measures of the two sides:
10 + 12 > c
c < 22
Therefore, the length of the third side must be less than 22.
However, since we are considering a scalene triangle, the length of the third side cannot be equal to the sum of the other two sides.
Thus, we can conclude that the length of the third side will be greater than the difference between the lengths of the two given sides. Since the difference between the lengths of the sides is 2, the length of the third side needs to be greater than 2.
Therefore, the possible length of the third side of the scalene triangle must be greater than 2 and less than 22.
To determine the length of the third side of a scalene triangle when two sides are given, we can use the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Therefore, to find the possible length of the third side, we need to check if the sum of the given sides is greater than the length of the third side.
In this case, the given sides are 10 and 12. Let's assume that the length of the third side is "x."
Using the triangle inequality theorem, we can write the following inequality:
(10 + 12) > x
Simplifying this inequality, we get:
22 > x
Therefore, the length of the third side must be less than 22 units.
To determine the exact range of possible lengths for the third side, we need additional information. The triangle inequality theorem does not provide a specific value, only the upper limit.