the measure of two sides of a triangle are 15 and 18. Between what two numbers must the measure of the third side fall?
The sum and the difference: 3 and 33.
Try to draw a triangle with third side length outside that range. It cannot be done. 3 and 33 correspond to having all vertexes along a straight line.
Tatti, poti, टट्टी , पौटी
To determine between what two numbers the measure of the third side of a triangle must fall, 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.
Let's use this theorem to find the range for the length of the third side:
1. Let's assume that the two given sides are 15 and 18.
2. We add the two given sides: 15 + 18 = 33.
3. To find the upper limit of the third side, we subtract the smaller given side from the sum of the given sides: 33 - 15 = 18.
4. To find the lower limit of the third side, we subtract the larger given side from the sum of the given sides: 33 - 18 = 15.
Therefore, the measure of the third side must fall between 15 and 18.
To find out between which two numbers the measure of the third side of a triangle must fall, 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.
In this case, the given lengths of the two sides are 15 and 18. Let's assume the third side has a length of x. So, we have the following inequality:
15 + 18 > x
To simplify this inequality, we add 15 and 18:
33 > x
Therefore, the measure of the third side must be less than 33. However, to find the upper bound of the third side, we need to consider the other inequality. The triangle inequality theorem also states that the difference between the lengths of any two sides of a triangle must be less than the length of the third side.
In this case, we can set up the following inequality:
18 - 15 < x
Simplifying this inequality, we get:
3 < x
Therefore, the measure of the third side must be greater than 3.
Combining both inequalities, we conclude that the measure of the third side must fall between 3 and 33.