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Chapter 0: Problem 3

Find the perimeter and area of a rectangle whose dimensions are 6 in. by 12 in.

Short Answer

Expert verified
Perimeter = 36 inches, Area = 72 square inches.

Step by step solution

01

- Identify the dimensions

The dimensions of the rectangle are given as 6 inches and 12 inches.
02

- Calculate the perimeter

The formula for the perimeter of a rectangle is: \[ P = 2(l + w) \] where \( l \) is the length and \( w \) is the width. Substituting the given values: \[ P = 2(12 + 6) = 2(18) = 36 \text{ inches} \]
03

- Calculate the area

The formula for the area of a rectangle is: \[ A = l \times w \] Substituting the given values: \[ A = 12 \times 6 = 72 \text{ square inches} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

rectangle dimensions
To solve problems involving the perimeter and area of a rectangle, you first need to understand its dimensions.
A rectangle has two length sides and two width sides.
The length is the longer side, while the width is the shorter side.
In our exercise, the rectangle's length is 12 inches and its width is 6 inches.
Always label your dimensions clearly to avoid mistakes.
Remember, in rectangles, opposite sides are equal.
So, if one side measures 12 inches, the side directly opposite will also measure 12 inches.
Similarly, if one side measures 6 inches, the side opposite will also measure 6 inches.
perimeter formula
The perimeter of a rectangle is the total distance around the outside of the shape.
To find it, you can use the formula: \( P = 2(l + w) \)
Here, \( P \) represents the perimeter, \( l \) stands for length, and \( w \) stands for width.
You simply add the length and width together, then multiply the sum by 2.
For our rectangle with dimensions 12 inches and 6 inches:
\( P = 2(12 + 6) = 2(18) = 36 \text{ inches} \)
So, the perimeter of the rectangle is 36 inches.
This formula works because you are combining the lengths of all four sides.
area formula
The area of a rectangle tells us how much space is inside the shape.
To calculate the area, use the formula: \( A = l \times w \)
Where \( A \) denotes the area, \( l \) is the length, and \( w \) is the width.
Multiply the length by the width to find the area.
For the given rectangle with 12-inch length and 6-inch width:
\( A = 12 \times 6 = 72 \text{ square inches} \)
Thus, the area of our rectangle is 72 square inches.
This formula shows how the space inside the rectangle is calculated by considering its two dimensions.

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