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.