The area of a rectangle is 30ft sqaure
Express P, the perimeter of the rectangle (in feet) as a function of its width  (in feet).

Given that the area \( A \) of the rectangle is 30 square feet, we can express the perimeter \( P \) of the rectangle as a function of its width \( w \).

1. **Area formula**: 
   \[
   A = l \times w
   \]
   where \( l \) is the length and \( w \) is the width. Since \( A = 30 \) square feet, we have:
   \[
   l \times w = 30
   \]
   Therefore, the length \( l \) can be expressed as:
   \[
   l = \frac{30}{w}
   \]

2. **Perimeter formula**: 
   The perimeter \( P \) of a rectangle is given by:
   \[
   P = 2l + 2w
   \]
   Substituting \( l = \frac{30}{w} \) into the perimeter formula:
   \[
   P = 2\left(\frac{30}{w}\right) + 2w
   \]
   Simplifying:
   \[
   P = \frac{60}{w} + 2w
   \]

Thus, the perimeter \( P \) as a function of width \( w \) is:
\[
P(w) = \frac{60}{w} + 2w
\]

Would you like more details or further explanation on any step?

Here are some related questions for further exploration:
1. What is the perimeter of the rectangle if the width is 5 feet?
2. How does the function behave as the width becomes very small?
3. How does the function behave as the width becomes very large?
4. How can we find the minimum perimeter for this rectangle?
5. What are the dimensions of the rectangle if the perimeter is 40 feet?

**Tip**: When working with perimeter and area formulas, it's helpful to remember the geometric relationships between the dimensions of the shapes!

The area of a rectangle is 30ft square. Express P, the perimeter of the rectangle (in feet) as a function of its width (in feet).

Learn how to express the perimeter of a rectangle with an area of 30 square feet as a function of its width. This problem involves the geometric properties of rectangles, including the area-perimeter relationship and algebraic expressions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation