RT
. Given S, T, equals, 7ST=7 and R, S, equals, 5, commaRS=5, determine the length start overline, R, T, end overline, .
RT
.

To determine the length of line segment \( \overline{RT} \), we're given the following information:

1. \( RS = 5 \), which means the length of the line segment between points \( R \) and \( S \) is 5 units.
2. \( ST = 7 \), which means the length of the line segment between points \( S \) and \( T \) is 7 units.
3. We want to determine \( RT \), the length of the line segment between points \( R \) and \( T \).

Now, to calculate \( RT \), we need to know if these three points \( R \), \( S \), and \( T \) are collinear, meaning they lie on a straight line. If they are collinear, the total length \( RT \) would simply be the sum of the individual segments:

\[
RT = RS + ST = 5 + 7 = 12
\]

So, if \( R \), \( S \), and \( T \) are collinear, the length of \( \overline{RT} \) is 12 units.

If they are not collinear, additional information such as the angle between the segments or the coordinates of the points would be needed to use the Pythagorean theorem or trigonometry.

Would you like to explore more on this? Here are some related questions:

1. What if \( R \), \( S \), and \( T \) are not collinear?
2. How do you calculate lengths in non-collinear situations?
3. What methods can be used to find angles between line segments?
4. Can this problem be solved using vector geometry?
5. How would this calculation change in 3-dimensional space?

**Tip:** When points are collinear, the total distance between the two farthest points is the sum of the intermediate segments.

Given S, T = 7 and R, S = 5, determine the length of RT.

Learn how to calculate the length of line segment RT given RS = 5 and ST = 7. This geometry problem explores collinear points and the sum of line segments. Suitable for students in Grades 6-8.

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