Write both the product and sum expression for the rectangle below:
Understand the Problem
The question is asking for the product and sum expressions based on a rectangle with given dimensions. The dimensions are 2x and 3 for one side, and 4 for the other. This involves understanding how to express these values mathematically.
Answer
Product: $(2x + 3) \times 4$; Sum: $2 \times [(2x + 3) + 4]$
Answer for screen readers
Product expression: $(2x + 3) \times 4$
Sum expression: $2 \times [(2x + 3) + 4]$
Steps to Solve
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Identify the Expressions for Dimensions The rectangle has two dimensions that can be seen on one side: $2x$ and $3$, with the height being $4$.
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Calculate the Product Expression The product expression represents the area of the rectangle. The area $A$ can be calculated using the formula:
$$ A = \text{width} \times \text{height} $$
In this case, the width can be considered as $2x + 3$, and the height as $4$. Therefore:
$$ A = (2x + 3) \times 4 $$
- Calculate the Sum Expression The sum expression will represent the total measure of all sides of the rectangle. To find the perimeter $P$ of the rectangle, we can use the formula:
$$ P = 2 \times (\text{width} + \text{height}) $$
Here, the width is $2x + 3$ and the height is $4$. Thus:
$$ P = 2 \times [(2x + 3) + 4] $$
Product expression: $(2x + 3) \times 4$
Sum expression: $2 \times [(2x + 3) + 4]$
More Information
The product represents the area of the rectangle, while the sum represents the perimeter. Understanding these concepts is essential in geometry, particularly when dealing with shapes and dimensions.
Tips
- Failing to combine dimensions correctly: Some might forget to sum the dimensions for the width before multiplying.
- Misapplying formulas: It's important to use the correct formulas for area and perimeter.
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