A parallelogram has a perimeter of 96 inches, and 1 of its sides measures 16 inches. If it can be determined. What are the lengths, in inches, of the other 3 sides?

Options

A. 16, 16, 48
B. 16,24, 24
C. 16,32,32
D. 16,40,40

Answer

To solve the problem, we need to determine the lengths of the sides of the parallelogram given its perimeter and one side length.

### Step-by-step Solution:

1. **Understanding the Properties of a Parallelogram**:
A parallelogram has opposite sides that are equal in length. If we denote one side as \( x \) and the other side as \( y \), then the lengths of the sides can be represented as \( x, x, y, y \).

2. **Setting Up the Perimeter Equation**:
The perimeter \( P \) of a parallelogram is given by the formula:
\[ P = 2x + 2y \]
We know from the problem that the perimeter is 96 inches, so we can write:
\[ 2x + 2y = 96 \]

3. **Substituting the Known Side Length**:
We are given that one of the sides measures 16 inches. Let's assign \( x = 16 \). Now we can substitute \( x \) into the perimeter equation:
\[ 2(16) + 2y = 96 \]

4. **Calculating the Value of \( y \)**:
Simplifying the equation:
\[ 32 + 2y = 96 \]
Next, we isolate \( 2y \) by subtracting 32 from both sides:
\[ 2y = 96 - 32 \]
\[ 2y = 64 \]
Now, divide both sides by 2 to find \( y \):
\[ y = \frac{64}{2} = 32 \]

5. **Listing the Lengths of All Sides**:
Now that we have both side lengths, we can summarize:
- One side \( x = 16 \) inches
- The other side \( y = 32 \) inches
Therefore, the lengths of the sides of the parallelogram are:
- 16 inches (one side)
- 32 inches (the other side)
- 32 inches (the opposite side)
- 16 inches (the opposite side)

### Final Answer:
The lengths of the other three sides of the parallelogram are 16 inches, 32 inches, and 32 inches.