0. Two adjacent sides AB and BC of a parallelogram ABCD are in the ratio 5 : 3. If the perimeter is 320 cm, what is the length of AB and BC?

Given a parallelogram \(ABCD\) with adjacent sides \(AB\) and \(BC\) in the ratio \(5:3\), and a perimeter of \(320 \, \text{cm}\), we need to find the lengths of \(AB\) and \(BC\).

### Step 1: Define Variables for the Sides
Let:
- \(AB = 5x\)
- \(BC = 3x\)

### Step 2: Use the Perimeter Formula
The perimeter of a parallelogram is given by the formula:
\[
\text{Perimeter} = 2(AB + BC)
\]

Substituting the given values:
\[
320 = 2(5x + 3x)
\]

Simplify:
\[
320 = 2(8x) = 16x
\]

### Step 3: Solve for \(x\)
\[
16x = 320
\]
\[
x = \frac{320}{16} = 20
\]

### Step 4: Find the Lengths of \(AB\) and \(BC\)
Now, substitute \(x = 20\) into the expressions for \(AB\) and \(BC\):
- \(AB = 5x = 5 \times 20 = 100 \, \text{cm}\)
- \(BC = 3x = 3 \times 20 = 60 \, \text{cm}\)

### Final Answer:
- The length of \(AB\) is \(100 \, \text{cm}\).
- The length of \(BC\) is \(60 \, \text{cm}\).

Would you like any further explanations or details?

Here are some related questions:
1. How do you find the sides of a rectangle if its perimeter and side ratio are given?
2. What are the formulas for the perimeter and area of a parallelogram?
3. How does the ratio of sides affect the shape of a parallelogram?
4. What are the properties of parallelograms regarding side lengths?
5. Can the ratio of diagonals in a parallelogram be used to find side lengths?

**Tip:** In parallelograms, using the ratio of sides can simplify calculations, especially when combined with known perimeter or area values.

Learn how to calculate the lengths of sides AB and BC of a parallelogram ABCD with a ratio of 5:3 and a perimeter of 320 cm. This problem involves applying the perimeter formula of a parallelogram and understanding ratios in geometry. Suitable for Grades 7-9 students.

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