https://r2.erweima.ai/mathbot/image/1721807338975s1jv5nno.jpeg

To solve the problem, let's go through each part step-by-step.

### Part 1: Writing an equation that represents the height of the door in centimeters (\( h \)) based on the width of the base in centimeters (\( b \))

Given:
- The area of the rectangular pet door is \( 900 \) square centimeters.
- The area of a rectangle is calculated by multiplying its width (\( b \)) and height (\( h \)).

The equation for the area \( A \) of a rectangle is:
\[ A = b \cdot h \]

Here, the area \( A \) is \( 900 \) square centimeters:
\[ 900 = b \cdot h \]

To express the height (\( h \)) in terms of the width (\( b \)), we solve for \( h \):
\[ h = \frac{900}{b} \]

### Part 2: Finding the height when the base is 25 centimeters wide

Given:
- Width (\( b \)) = 25 centimeters

Using the equation derived:
\[ h = \frac{900}{b} \]

Substitute \( b = 25 \):
\[ h = \frac{900}{25} \]

Calculate the height:
\[ h = 36 \text{ centimeters} \]

Therefore, the height of the door is \( 36 \) centimeters when the base is \( 25 \) centimeters wide.

---

Do you have any questions or need further details on this solution?

Here are 5 more questions you might want to explore:
1. What would the height be if the width is 30 centimeters?
2. How would the equation change if the area were 1000 square centimeters instead?
3. If the width of the door is doubled, how does that affect the height?
4. What is the width of the door if the height is 20 centimeters?
5. How would you graph the relationship between the width and height of the door?

**Tip:** When working with area and dimensions, always ensure your units are consistent and remember the basic geometric formulas.

Learn how to solve the problem of finding the height of a pet door based on its width. This problem involves calculating the height of a rectangular pet door with a given area of 900 square centimeters. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation