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Let's solve the problem.

The perimeter of quadrilateral \( J K L M \) is given as 90 cm. The sides are labeled in the diagram as follows:
- \( J K = n + 7 \)
- \( K L = n \)
- \( L M = 2n - 12 \)
- \( M J = 3n + 4 \)

The perimeter is the sum of all the sides, so we have:
\[
(n + 7) + n + (2n - 12) + (3n + 4) = 90
\]

Now, simplify the expression:
\[
n + 7 + n + 2n - 12 + 3n + 4 = 90
\]
\[
7n - 1 = 90
\]
Add 1 to both sides:
\[
7n = 91
\]
Solve for \( n \):
\[
n = \frac{91}{7} = 13
\]

Now that we know \( n = 13 \), we can find the length of side \( K L \):
\[
K L = n = 13 \, \text{cm}
\]

Thus, the length of side \( K L \) is **13 cm**.

Would you like more details or explanations? Here are five related questions to expand your understanding:

1. What is the length of side \( J K \) when \( n = 13 \)?
2. What is the length of side \( L M \) when \( n = 13 \)?
3. What is the length of side \( M J \) when \( n = 13 \)?
4. How does changing the perimeter affect the value of \( n \)?
5. How do we verify that the total perimeter is 90 cm after calculating all sides?

**Tip:** Always double-check each part of your equation after solving for \( n \) to ensure the calculations are correct.

The perimeter of quadrilateral JKLM is 90 centimeters. Which is the length of side KL?

Learn how to solve for the length of side KL in quadrilateral JKLM with a perimeter of 90 cm. This math problem involves algebraic concepts and the use of linear equations. Suitable for students in Grades 7-9.

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