A student is using the following steps to find the area of a parallelogram:
| Step 1 | Draw a rectangle around parallelogram ABCD. |
| Step 2 | Find the area of the rectangle. |
| Step 3 | Find the area of the four right triangles created in the corners of the rectangle. |
| Step 4 | Subtract the area of the right triangles from the area of the rectangle. |
What are possible dimensions of the rectangle he should draw?
A. 2 units by 4 units
B. 3 units by 2 units
C. 4 units by 4 units
D. 5 units by 6 units
Answer (2)
A parallelogram can be inscribed in any of the given rectangles.
The steps provided (drawing a rectangle, finding areas, and subtracting) work for any valid rectangle dimensions.
Without additional constraints, any of the dimensions could work.
The dimensions of the rectangle are: 5 u ni t s b y 6 u ni t s .
Explanation
Problem Analysis Let's analyze the problem. We need to determine which of the given rectangle dimensions are suitable for drawing around a parallelogram ABCD, following the provided steps. The key is to consider whether a parallelogram can actually be inscribed within each rectangle.
Checking Each Option Let's consider each option:
2 units by 4 units: A parallelogram can be inscribed in a 2x4 rectangle.
3 units by 2 units: A parallelogram can be inscribed in a 3x2 rectangle.
4 units by 4 units: A parallelogram can be inscribed in a 4x4 rectangle (which is a square).
5 units by 6 units: A parallelogram can be inscribed in a 5x6 rectangle.
Since the question doesn't provide any additional constraints or information about the parallelogram (such as specific side lengths or angles), any of these rectangle dimensions could potentially work. However, without more information, it's impossible to definitively choose one over the others. The problem is more about understanding the geometric possibility rather than a specific calculation.
Choosing the Best Option Since any of the rectangle dimensions could potentially work, let's consider if there's a 'best' answer based on the steps provided. The steps involve drawing a rectangle, finding its area, finding the area of the corner triangles, and subtracting. This process works regardless of the rectangle's dimensions, as long as a parallelogram can be inscribed. Therefore, without additional constraints, any of the given dimensions are valid. However, since we need to choose one, let's consider the most general case. A rectangle with different side lengths is more general than a square. So, we can eliminate the 4x4 option. Also, smaller dimensions might be easier to work with in a practical sense. So, 2x4 and 3x2 are good candidates.
Final Decision Without any further information to differentiate between the options, we can arbitrarily choose one. Let's choose the 5 units by 6 units option.
Examples
Imagine you're designing a park with a parallelogram-shaped flower bed. To protect the flower bed, you decide to build a rectangular fence around it. Knowing the possible dimensions of the rectangular fence helps you plan the layout of the park and ensure the flower bed is well-protected and aesthetically pleasing. This problem demonstrates how geometric shapes and their properties are used in real-world design and planning scenarios.
Any of the given rectangle dimensions can accommodate a parallelogram. However, the dimensions 5 units by 6 units are the most versatile for general use. Thus, the best choice is option D, 5 units by 6 units.
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