To solve this problem, we need to determine the perimeter of the rectangular pool.

Understanding the Problem

• Width: $n$
• Length: $4n + 3$ (since the length is 3 more than 4 times the width).

The perimeter $P$ of a rectangle is given by:
$P = 2 \times (\text{Length} + \text{Width})$

Substitute the Values

Substitute $\text{Length} = 4n + 3$ and $\text{Width} = n$ into the formula:
$P = 2 \times ((4n + 3) + n)$ Simplify the expression inside the parentheses:
$P = 2 \times (4n + n + 3)$ $P = 2 \times (5n + 3)$ Distribute the $2$:
$P = 10n + 6$

Compare with the Answer Choices

Now let’s match this expression to the options:

• Option B: $2(5n + 3)$ → This matches because it simplifies to $10n + 6$. ✅
• Option E: $10n + 6$ → This directly matches our simplified perimeter expression. ✅

Final Answer

The correct options are:

• B: $2(5n + 3)$
• E: $10n + 6$

Would you like further clarification on any steps? Let me know!

Related Questions

1. How do you calculate the perimeter of a rectangle given its dimensions?
2. If the width is doubled, how would the perimeter change?
3. How would the expression change if the length was $3n + 2$ instead of $4n + 3$?
4. How do you determine the area of the same rectangular pool?
5. What happens to the perimeter if the width $n$ increases by 1 unit?

Tip: Always simplify expressions step by step when solving for geometric formulas like perimeter or area!