Question

The perimeter of the parallelogram to the right is 89.6. The length of side JM overbar is 15.2. 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.
Part 2
The length of JK overbar is
  
enter your response here.
Part 3
The length of ML overbar is
  
enter your response here.

Answer 1

To find the lengths of the other sides of the parallelogram, we can use the given information about the perimeter and one side's length.

1. The perimeter \( P \) of a parallelogram is calculated using the formula:
\[
P = 2( \text{length} + \text{width})
\]
In this case, we know that:
\[
P = 89.6
\]
and the length of one side (JM) is:
\[
\text{length} = 15.2
\]
Let's denote the unknown side (KL) as \( x \).

2. The perimeter equation can be set up as:
\[
89.6 = 2(15.2 + x)
\]

3. To simplify, divide both sides by 2:
\[
44.8 = 15.2 + x
\]

4. Now, isolate \( x \):
\[
x = 44.8 - 15.2 = 29.6
\]

Now, we have determined that \( KL = 29.6 \).

Since opposite sides of a parallelogram are equal, we have:
- \( KL = ML = 29.6 \) (as KL and ML are opposite sides).
- \( JK = JM = 15.2 \) (as JM and JK are opposite sides).

Now we can summarize the lengths:
- Part 1: The length of \( KL \overbar \) is **29.6**.
- Part 2: The length of \( JK \overbar \) is **15.2**.
- Part 3: The length of \( ML \overbar \) is **29.6**.