Question
This triangle has one side length of 4 inches and one of 7 inches.
Record the third side length in the table when the sides are put together like this. You can watch the video to find the third side length.
First Side
Length (inches) Second Side
Length (inches) Third Side
Length (inches)
4 7
Record the third side length in the table when the sides are put together like this. You can watch the video to find the third side length.
First Side
Length (inches) Second Side
Length (inches) Third Side
Length (inches)
4 7
Answers
GPT-4o mini
In a triangle, the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.
Given the two sides of lengths 4 inches and 7 inches, we can determine the possible lengths for the third side (let's call it \( x \)) using the triangle inequality:
1. The sum of the lengths of the two smaller sides must be greater than the length of the third side:
\( 4 + 7 > x \)
\( 11 > x \)
So, \( x < 11 \).
2. The sum of the length of one side and the length of the third side must be greater than the length of the other side (4):
\( 4 + x > 7 \)
\( x > 3 \).
3. The sum of the length of the other side and the length of the third side must be greater than the length of the first side (7):
\( 7 + x > 4 \)
This inequality is always true, because any positive value of \( x \) will satisfy it.
Combining these inequalities, we get:
\( 3 < x < 11 \).
Therefore, the possible lengths for the third side must be greater than 3 inches and less than 11 inches. You will need to measure or find an accurate value for the third side length within that range.
For your table:
| First Side Length (inches) | Second Side Length (inches) | Third Side Length (inches) |
|-----------------------------|------------------------------|-----------------------------|
| 4 | 7 | (between 3 and 11, e.g., any value like 5, 6, 8, etc.) |
If you watched a video that shows a specific measurement, please record that precise value in the third column.
Given the two sides of lengths 4 inches and 7 inches, we can determine the possible lengths for the third side (let's call it \( x \)) using the triangle inequality:
1. The sum of the lengths of the two smaller sides must be greater than the length of the third side:
\( 4 + 7 > x \)
\( 11 > x \)
So, \( x < 11 \).
2. The sum of the length of one side and the length of the third side must be greater than the length of the other side (4):
\( 4 + x > 7 \)
\( x > 3 \).
3. The sum of the length of the other side and the length of the third side must be greater than the length of the first side (7):
\( 7 + x > 4 \)
This inequality is always true, because any positive value of \( x \) will satisfy it.
Combining these inequalities, we get:
\( 3 < x < 11 \).
Therefore, the possible lengths for the third side must be greater than 3 inches and less than 11 inches. You will need to measure or find an accurate value for the third side length within that range.
For your table:
| First Side Length (inches) | Second Side Length (inches) | Third Side Length (inches) |
|-----------------------------|------------------------------|-----------------------------|
| 4 | 7 | (between 3 and 11, e.g., any value like 5, 6, 8, etc.) |
If you watched a video that shows a specific measurement, please record that precise value in the third column.