Question

The perimeter of the parallelogram to the right is 74.6. The length of side JM overbar is 16.8. Find the lengths of KL overbar​, JK overbar​, and ML overbar.
Question content area bottom left
Part 1
The length of KL overbar is
  
16.8.
Part 2
The length of JK overbar is
  
enter your response here.

Answer 1

In a parallelogram, opposite sides are equal in length. Therefore:

1. Since \( JM \) (one side) is \( 16.8 \), then the opposite side \( KL \) is also \( 16.8 \).
2. The perimeter \( P \) of a parallelogram is calculated as:
\[
P = 2 \times (\text{length of one side} + \text{length of the adjacent side})
\]

Given that the perimeter \( P \) is \( 74.6 \), you can set up the equation as follows:
\[
74.6 = 2 \times (JM + JK)
\]
Substituting the value of \( JM \):
\[
74.6 = 2 \times (16.8 + JK)
\]

Next, simplify:
\[
74.6 = 33.6 + 2 \times JK
\]
Subtract \( 33.6 \) from both sides:
\[
41.0 = 2 \times JK
\]
Now, divide by \( 2 \):
\[
JK = \frac{41.0}{2} = 20.5
\]

Since in parallelograms, opposite sides are also equal, the length of \( ML \) is equal to \( JK \), which is \( 20.5 \).

### Summary:
- The length of \( KL \) is \( 16.8 \).
- The length of \( JK \) is \( 20.5 \).
- The length of \( ML \) is \( 20.5 \).