The expressions x – 2 and x +3 represent the length and width of a rectangle, respectively. If the area of the rectangle is 24, what is the perimeter of the rectangle? O 20 O 22 O 24 O 28 O O O O
The expressions x – 2 and x +3 represent the length and width of a rectangle, respectively. If the area of the rectangle is 24, what is the perimeter of the rectangle? O 20 O 22 O 24 O 28 O O O O
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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
Transcribed Image Text:### Instructions
Choose the best answer. If necessary, use the paper you were given.
### Question
The expressions \(x - 2\) and \(x + 3\) represent the length and width of a rectangle, respectively. If the area of the rectangle is 24, what is the perimeter of the rectangle?
- ○ 20
- ○ 22
- ○ 24
- ○ 28
### Explanation for Educators:
This question tests the understanding of algebraic expressions in geometry, specifically relating to the area and perimeter of rectangles. The student is required to:
1. Set up the equation for the area of the rectangle using the given expressions.
2. Solve for \(x\).
3. Calculate the length and width of the rectangle.
4. Determine the perimeter using the found dimensions.
Step-by-step guide:
- The given expressions for length and width are \(x - 2\) and \(x + 3\), respectively.
- Set up the area equation: \((x - 2)(x + 3) = 24\).
- Solve this quadratic equation for \(x\).
- Once \(x\) is found, substitute back into \(x - 2\) and \(x + 3\) to find the length and width.
- Finally, use the perimeter formula \(P = 2 \times (\text{Length} + \text{Width})\).
By following these steps, students should be able to identify the correct multiple-choice answer.
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