The area of a rectangle is 402in2
.  If the length of the rectangle is x inches, write a function for the perimeter, P(x)
.

Given that the area of a rectangle is \( 402 \) square inches, and the length of the rectangle is \( x \) inches, you want to express the perimeter \( P(x) \) as a function of \( x \).

### Step 1: Express the width in terms of \( x \)

The area \( A \) of the rectangle is given by:
\[
A = \text{length} \times \text{width} 
\]
\[
402 = x \times \text{width} 
\]
\[
\text{width} = \frac{402}{x}
\]

### Step 2: Write the formula for the perimeter

The perimeter \( P \) of a rectangle is given by:
\[
P = 2 \times (\text{length} + \text{width})
\]
Substituting the given length \( x \) and the expression for width:
\[
P(x) = 2 \times \left(x + \frac{402}{x}\right)
\]

So, the function for the perimeter in terms of \( x \) is:
\[
P(x) = 2 \left(x + \frac{402}{x}\right)
\]

### Summary
The function for the perimeter of the rectangle is:
\[
P(x) = 2 \left(x + \frac{402}{x}\right)
\]

Do you want any more details or have any questions?

---

Here are 8 related questions for further practice:

1. What is the perimeter if the length \( x \) is 10 inches?
2. How would you find the minimum perimeter for the rectangle?
3. What is the width of the rectangle if the length is 15 inches?
4. How does the perimeter change as \( x \) increases?
5. What is the derivative of the perimeter function \( P(x) \)?
6. If the length and width are equal, what would be the dimensions of the square with an area of 402 square inches?
7. How would you express the perimeter function in terms of the width instead of the length?
8. Can you find the dimensions that minimize the perimeter for a fixed area of 402 square inches?

**Tip:** When working with functions, always check the domain to ensure your solution is valid for all possible values of \( x \).

Learn how to calculate the perimeter of a rectangle with an area of 402 square inches using algebraic expressions. Understand the relationship between length, width, area, and perimeter in geometry problems. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation