Exploring the Rectangle's Dimensions: Area, Perimeter, and Key Formulas

To understand the relationship between the dimensions of a rectangle, we often use the formulas for area and perimeter. These formulas help us find or verify the length and breadth of a rectangle given certain measurements.

Given the Area and Length, Find the Breadth

Question: If the area of a rectangle is 36 square centimeters (cm^2) and the length is 9 cm, what is the breadth?

Step-by-Step Solution

Recall the formula for the area of a rectangle: Area Length × Breadth. Substitute the known values into the formula: 36 cm^2 9 cm × Breadth. Solve for the breadth:

Breadth 36 cm^2 ÷ 9 cm 4 cm.

Therefore, the breadth of the rectangle is 4 cm.

What Happened in the Given Problem?

A guess was made where the length was said to be 10 cm, and the breadth was supposed to be 'z'. However, the correct steps were provided to solve the problem, which simplifies to the correct breadth being 9 cm.

Correct Values and Methods

Length 9 cm Area 72 cm^2 Use the formula: Area Length × Breadth Solve for Breadth: Breadth Area ÷ Length 72 cm^2 ÷ 9 cm 8 cm Thus, the breadth is 8 cm.

Understanding the Perimeter in Relation to the Breadth and Given Area

For a more complex example, consider a perimeter that is supposed to be 36 cm, which could be misleading as perimeters are measured in linear units, not square units. However, using the relation: Perimeter 2(Length Breadth), we can find the correct breadth if we have the correct values.

Steps to Verify the Correct Breadth Given Incorrectly Stated Perimeter

Given Length 9 cm and Area 72 cm^2. Use the formula for area to find the breadth: Breadth 72 cm^2 ÷ 9 cm 8 cm. Verify the given perimeter statement, if Perimeter 36 cm, then the initial perimeter statement of 202z 36 cm is incorrect, as perimeter cannot be represented in square units. Correctly, the perimeter 2(9 cm 8 cm) 34 cm, which is closer to a reconcilable value.

Conclusion and Further Study

To further explore the relationship between the dimensions of a rectangle, it's crucial to use the correct formulas and units. Whether you are interested in the area, perimeter, or other properties of rectangles, understanding these basic principles is essential.

Key Takeaways

The area of a rectangle is calculated by multiplying the length and the breadth. The perimeter is calculated by summing the lengths of all four sides, or twice the sum of the length and breadth. Always ensure you use the correct units for each measurement to avoid confusion.