Let the length and width of the rectangle be $5x$ and $3x$ respectively, as they are in the ratio $5:3$.

Step 1: Area of the Rectangle

The area of the rectangle is given as $375 \, \text{m}^2$. Using the formula for the area of a rectangle:

$\text{Area} = \text{Length} \times \text{Width}$

$375 = (5x)(3x)$

$375 = 15x^2$

Step 2: Solve for $x^2$

Divide both sides of the equation by $15$:

$x^2 = \frac{375}{15} = 25$

Taking the square root of both sides:

$x = \sqrt{25} = 5$

Step 3: Length and Width

Now, substitute $x = 5$ back into the expressions for length and width:

$\text{Length} = 5x = 5 \times 5 = 25 \, \text{m}$

$\text{Width} = 3x = 3 \times 5 = 15 \, \text{m}$

Step 4: Perimeter of the Rectangle

The perimeter of a rectangle is given by:

$\text{Perimeter} = 2(\text{Length} + \text{Width})$

Substitute the values of length and width:

$\text{Perimeter} = 2(25 + 15) = 2(40) = 80 \, \text{m}$

Final Answer:

The perimeter of the rectangle is:

$\boxed{80 \, \text{m}}$

Would you like a detailed explanation of any part?

Related Questions:

1. If the length were increased by 20%, what would be the new area?
2. What is the diagonal of the rectangle in meters?
3. What is the ratio of the perimeter to the width?
4. If the width is reduced by 5 m, what would be the new perimeter?
5. Can you express the perimeter as a function of the area?

Tip:

When solving problems with ratios, always assign variables carefully to avoid confusion.