In geometry, area and perimeter are fundamental concepts that define the properties of two-dimensional shapes. ...
Area refers to the amount of space a shape occupies. It is measured in square units, such as square centimeters (cm²) or square inches (in²). For a rectangle, the area is calculated by multiplying its length and width:
Area of Rectangle = Length x Width
Perimeter, on the other hand, refers to the total distance around the outside of a shape. It is measured in linear units, such as centimeters (cm) or inches (in). The perimeter of a rectangle is calculated by adding up the lengths of all its sides:
Perimeter of Rectangle = 2 x (Length + Width)
The Problem: Comparing Rectangles A and B
We are presented with two rectangles, A and B, with the following dimensions:
- Rectangle A: Length = 12 cm, Width = 2 cm
- Rectangle B: Length = 4 cm, Width = ?
We know that the area of Rectangle A is equal to the area of Rectangle B. Our task is to determine which rectangle has the greater perimeter and by how much.
Calculating the Area and Width of Rectangle B
Let's first calculate the area of Rectangle A:
Area of Rectangle A = 12 cm x 2 cm = 24 cm²
Since the area of Rectangle A is equal to the area of Rectangle B, we can find the width of Rectangle B:
Area of Rectangle B = 24 cm²
Area of Rectangle B = Length x Width
24 cm² = 4 cm x Width
Width = 24 cm² / 4 cm = 6 cm
Calculating the Perimeter of Rectangles A and B
Now, we can calculate the perimeter of each rectangle:
Perimeter of Rectangle A = 2 x (12 cm + 2 cm) = 28 cm
Perimeter of Rectangle B = 2 x (4 cm + 6 cm) = 20 cm
Determining the Greater Perimeter
Comparing the perimeters, we find that Rectangle A has a greater perimeter than Rectangle B:
Perimeter of Rectangle A - Perimeter of Rectangle B = 28 cm - 20 cm = 8 cm
Conclusion
Therefore, Rectangle A has a greater perimeter than Rectangle B by 8 centimeters. This demonstrates that even though two rectangles can have equal areas, their perimeters can differ significantly depending on their length and width. This concept is important in understanding the relationship between geometric properties and how they can be used in various practical applications.