Question

To find the perimeter \(P\) of a rectangle with length \(L\) and width \(W\), what is the correct formula? (A) \(P=L \times W \quad\) OR (B) \(P=2 L+2 W\)

Short answer

The correct formula for the perimeter of a rectangle is (B) \(P=2L+2W\).

Step-by-step solution

Understanding the Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around the outside, composed of two lengths and two widths.

Reviewing the Given Formulas

We have two options: (A) The formula given is \( P = L \times W \).(B) The formula given is \( P = 2L + 2W \).We need to determine which equation correctly represents the perimeter of a rectangle.

Analyzing Formula A

Formula (A) represents multiplication of length and width (\( P = L \times W \)), which actually calculates the area of the rectangle, not the perimeter.

Analyzing Formula B

Formula (B) represents the sum of all sides (\( P = 2L + 2W \)), calculating the total length around the rectangle, which is consistent with how perimeter is defined.

Conclusion

Formula (B), \( P = 2L + 2W \), fits the definition of perimeter as it considers both the length and width. Formula (A) is incorrect for calculating perimeter because it is used for area.

Key concepts

Geometry Formulas

In geometry, formulas are essential tools that help us calculate different measurements and dimensions of various shapes. For example:

• Formulas help compute areas, volumes, and perimeters.
• They allow us to translate real-world problems into mathematical terms.
• Understanding these formulas helps in problem-solving and applying the right equation depending on the need.

When it comes to rectangles, knowing the correct formula is crucial. The perimeter of a rectangle is calculated by adding all its sides, which leads us to the formula: \[ P = 2L + 2W \] Here, \(L\) represents the length and \(W\) represents the width. This formula efficiently tells us the total distance around the rectangle, covering both pairs of parallel sides. Meanwhile, the area of the rectangle is determined by: \[ A = L \times W \] Differentiating between these formulas ensures you apply the correct ones based on what you need to find.

Rectangle Properties

Rectangles hold certain properties that are key to understanding their geometric relevance:

• A rectangle has four sides.
• Opposite sides are equal in length and each angle measures 90 degrees.
• All rectangles are parallelograms, but not all parallelograms are rectangles.

Knowing these properties helps in applying correct measurements. For perimeter calculation:

• Measure both the length and the width of the rectangle.
• Because there are two lengths and two widths in a rectangle, the perimeter becomes straightforward using the formula \(P = 2L + 2W\).

Visualizing a rectangle helps in understanding that its perimeter is literally the path one would walk around if one were to "walk" around the rectangle once.

Mathematical Problem-Solving

Problem-solving in mathematics involves several steps:

• Understanding the problem.
• Choosing the correct formulas.
• Executing calculations accurately.

These steps are essential for tackling questions involving geometric shapes. When faced with a task like finding the perimeter of a rectangle, start by:

• Identifying given measurements (length and width).
• Selecting the correct formula for perimeter (\(P = 2L + 2W\)).
• Substituting the values into the formula.
• Performing the arithmetic to arrive at the correct perimeter value.

A logical approach reinforces understanding and boosts confidence in handling similar mathematical tasks or more complex geometrical problems in the future.