https://file.aiquickdraw.com/mathbot/file/1730989624187u8ho2hbf.jpg

To solve this problem, let's analyze the given information.

We have a parallelogram \( LMNO \) where the diagonals \( LN \) and \( MO \) intersect at point \( X \). In a parallelogram, the diagonals bisect each other. This means that \( LX = XN \) and \( MX = XO \).

### Given Data:
1. \( LX = 5 \, \text{cm} \)
2. \( MX = 6 \, \text{cm} \)

### Solution:
Since \( LX = XN \), the entire length of \( LN \) is:
\[
LN = LX + XN = 5 \, \text{cm} + 5 \, \text{cm} = 10 \, \text{cm}
\]

Similarly, since \( MX = XO \), the entire length of \( MO \) is:
\[
MO = MX + XO = 6 \, \text{cm} + 6 \, \text{cm} = 12 \, \text{cm}
\]

### Answer:
- The length of \( LN \) is \( 10 \, \text{cm} \).
- The length of \( MO \) is \( 12 \, \text{cm} \).

Would you like further clarification or have any questions?

Here are some additional questions related to this topic:
1. What would change if \( LX \) and \( MX \) were not equal halves of \( LN \) and \( MO \)?
2. How do we find the lengths of diagonals in a general quadrilateral, not necessarily a parallelogram?
3. What are the properties of diagonals in other shapes like rectangles, rhombuses, and squares?
4. How would the problem change if \( LX \) and \( MX \) were given as variables instead of specific values?
5. How does knowing that diagonals bisect each other help us determine side lengths in certain polygons?

**Tip:** Remember that the diagonals of a parallelogram bisect each other, meaning they divide each other into equal halves. This property is unique to parallelograms among quadrilaterals.

In parallelogram LMNO, the diagonals LN and MO intersect at point X. If LX = 5 cm and MX = 6 cm, find the lengths of LN and MO.

Learn how to find the lengths of diagonals in a parallelogram with given measurements for half-diagonals. This geometry problem demonstrates the properties of parallelograms and is suitable for Grade 8 students.

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