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.
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Part 1
The length of KL overbar is
  
enter your response here.

Answer 1

To find the lengths of the sides of the parallelogram given the perimeter and one side, we can use the properties of a parallelogram. In a parallelogram, opposite sides are equal, and the perimeter \( P \) is given by the formula:

\[
P = 2 \times (length + width)
\]

Let's break this down using the information you provided:

1. The perimeter \( P \) is 74.6.
2. The length of side \( JM \) (which we can assume corresponds to one of the sides of the parallelogram, let’s say the length \( JK \)) is 16.8.

Let’s denote:
- \( JK = JM = 16.8 \)
- Let \( KL \) (the other side) be denoted as \( x \).

Now we can set up the equation:

\[
P = 2 \times (JK + KL)
\]

Substituting the values we have:

\[
74.6 = 2 \times (16.8 + x)
\]

Now, divide both sides by 2:

\[
37.3 = 16.8 + x
\]

Now, solve for \( x \):

\[
x = 37.3 - 16.8 = 20.5
\]

Therefore, the length of \( KL \overline \) is \( 20.5 \).

### Summary of Lengths
- \( JK \overline = 16.8 \)
- \( KL \overline = 20.5 \)
- \( ML \overline \) (which is another side equal to \( JK \)) = \( 16.8 \)

### Final Answer
The length of \( KL \overline \) is **20.5**.