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A rectangle is formed by bending a wire that is 32 centimeters long. The length of the rectangle is 12 centimeters. What is the width, in centimeters, of the rectangle? 12 cm cm

A rectangle is formed by bending a wire that is 32 centimeters long. The length of the rectangle is 12 centimeters. What is the width, in centimeters, of the rectangle? 12 cm cm

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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## Rectangle Problem A rectangle is formed by bending a wire that is **32 centimeters** long. The length of the rectangle is **12 centimeters**. **Question:** What is the width, in centimeters, of the rectangle? ### Given Data: - Length of the wire: **32 cm** - Length of the rectangle: **12 cm** ### Solution: 1. Recall the formula for the perimeter (P) of a rectangle: \[ P = 2 \times ( \text{length} + \text{width} ) \] 2. Substitute the given values into the perimeter formula: \[ 32 = 2 \times ( 12 + \text{width} ) \] 3. Simplify the equation: \[ 32 = 24 + 2 \times \text{width} \] 4. Subtract 24 from both sides: \[ 8 = 2 \times \text{width} \] 5. Divide both sides by 2: \[ \text{width} = 4 \] Thus, the width of the rectangle is **4 centimeters**. ### Diagram Explanation: There is a visual representation of a rectangle with clearly marked dimensions. The length is indicated as **12 cm** and the width is represented as a blank space meant to be filled with the correct width value, which we've calculated as **4 cm**.
Transcribed Image Text:## Rectangle Problem A rectangle is formed by bending a wire that is **32 centimeters** long. The length of the rectangle is **12 centimeters**. **Question:** What is the width, in centimeters, of the rectangle? ### Given Data: - Length of the wire: **32 cm** - Length of the rectangle: **12 cm** ### Solution: 1. Recall the formula for the perimeter (P) of a rectangle: \[ P = 2 \times ( \text{length} + \text{width} ) \] 2. Substitute the given values into the perimeter formula: \[ 32 = 2 \times ( 12 + \text{width} ) \] 3. Simplify the equation: \[ 32 = 24 + 2 \times \text{width} \] 4. Subtract 24 from both sides: \[ 8 = 2 \times \text{width} \] 5. Divide both sides by 2: \[ \text{width} = 4 \] Thus, the width of the rectangle is **4 centimeters**. ### Diagram Explanation: There is a visual representation of a rectangle with clearly marked dimensions. The length is indicated as **12 cm** and the width is represented as a blank space meant to be filled with the correct width value, which we've calculated as **4 cm**.
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