https://file.aiquickdraw.com/mathbot/file/1726565787152406ubmzy.jpg

To find the length \( KL \), let's analyze the information given in the diagram:

1. The points on the line segment are \( J \), \( K \), \( L \), and \( M \), with \( K \) and \( L \) lying between \( J \) and \( M \).
2. The total length of \( JM \) is given as \( x + 31 \).
3. The segments are broken down as:
   - \( JK = 9 \)
   - \( KL = x + 16 \)
   - \( LM = x + 11 \)

According to the properties of line segments:
\[
JM = JK + KL + LM
\]
Substituting the given values:
\[
x + 31 = 9 + (x + 16) + (x + 11)
\]

Let's simplify this equation to find \( x \):

\[
x + 31 = 9 + x + 16 + x + 11
\]
\[
x + 31 = 2x + 36
\]

Subtract \( x \) from both sides:
\[
31 = x + 36
\]

Subtract 36 from both sides:
\[
31 - 36 = x
\]
\[
-5 = x
\]

Now that we have \( x = -5 \), we can find the length of \( KL \):
\[
KL = x + 16 = -5 + 16 = 11
\]

So, the length of \( KL \) is **11** units.

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. What would the length of \( LM \) be with this value of \( x \)?
2. How would the length of \( KL \) change if \( x \) were a different value?
3. What is the total length of \( JM \) using the calculated value of \( x \)?
4. Can the length of a line segment ever be negative? Why or why not?
5. How would you solve this if the total length \( JM \) was given in a different form?

**Tip:** Always check if the value of \( x \) makes sense within the context of the problem, especially in geometry where lengths must be positive.

Find KL for the line segment JM, where JK = 9, KL = x + 16, LM = x + 11, and JM = x + 31.

Learn how to find the length of KL in a line segment problem where JK = 9, KL = x + 16, LM = x + 11, and JM = x + 31. This solution involves solving for x and applying line segment properties. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation