Two sides of a triangle measure 3.7 and 8.2. Apply the Triangle Inequality Theorem to find a possible measure of the third side.
Pick one of the following choices.
1. 4.2
2. 3.5
3. 5.5
4. 4.5
5.5
1. 15
2. 5cm
3. 9
4. 2,7,6
5. 5.5
there is all the answers for you guys and girls.
To apply 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.
Let's apply the theorem to the given triangle:
Side 1: 3.7
Side 2: 8.2
Sum of Side 1 and Side 2: 3.7 + 8.2 = 11.9
Now, the length of the third side must be less than the sum of Side 1 and Side 2 but greater than the difference between them.
Now, let's consider the choices:
1. 4.2
2. 3.5
3. 5.5
4. 4.5
Of these choices, only 4.5 is greater than the difference (8.2 - 3.7 = 4.5) but less than the sum (11.9). Therefore, the possible measure of the third side is 4.5.
So, the answer is 4.5.
To apply the Triangle Inequality Theorem, we need to ensure that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Given that two sides of the triangle measure 3.7 and 8.2, we can test each answer choice by adding it to the length of either side and checking if it is greater than the length of the other side.
Let's go through each answer choice:
1. 4.2: When we add 4.2 to 3.7, we get 7.9, which is less than 8.2. Therefore, this is not a possible measure for the third side.
2. 3.5: When we add 3.5 to 3.7, we get 7.2, which is less than 8.2. Therefore, this is not a possible measure for the third side.
3. 5.5: When we add 5.5 to 3.7, we get 9.2, which is greater than 8.2. Therefore, this is a possible measure for the third side.
4. 4.5: When we add 4.5 to 3.7, we get 8.2, which is equal to 8.2. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides must be greater than the length of the third side, not equal to it. Therefore, this is not a possible measure for the third side.
Therefore, the correct answer is 3. 5.5.