Asked by abdelrahman almarzooqi
How can you determine the perimeter of a rectangle that is 3 cm wide and 5 cm long in two different ways? Which strategy do you think is more efficient?
Answers
Answered by
GPT-4o mini
To determine the perimeter of a rectangle with a width of 3 cm and a length of 5 cm, you can use two different methods:
### Method 1: Using the Perimeter Formula
The formula for the perimeter \( P \) of a rectangle is given by:
\[
P = 2 \times ( \text{length} + \text{width} )
\]
Substituting the given dimensions:
\[
P = 2 \times (5 \, \text{cm} + 3 \, \text{cm}) = 2 \times 8 \, \text{cm} = 16 \, \text{cm}
\]
### Method 2: Adding Each Side's Length Individually
You can also calculate the perimeter by adding the lengths of all four sides of the rectangle directly:
\[
P = \text{length} + \text{width} + \text{length} + \text{width}
\]
Substituting the dimensions:
\[
P = 5 \, \text{cm} + 3 \, \text{cm} + 5 \, \text{cm} + 3 \, \text{cm} = 16 \, \text{cm}
\]
### Which Strategy is More Efficient?
The first method, using the perimeter formula, is generally more efficient. It succinctly calculates the perimeter in one step and requires less arithmetic. The second method, while valid, involves more additions and may lead to more chances for error in calculations. Thus, using the formula is often quicker and simpler.
### Method 1: Using the Perimeter Formula
The formula for the perimeter \( P \) of a rectangle is given by:
\[
P = 2 \times ( \text{length} + \text{width} )
\]
Substituting the given dimensions:
\[
P = 2 \times (5 \, \text{cm} + 3 \, \text{cm}) = 2 \times 8 \, \text{cm} = 16 \, \text{cm}
\]
### Method 2: Adding Each Side's Length Individually
You can also calculate the perimeter by adding the lengths of all four sides of the rectangle directly:
\[
P = \text{length} + \text{width} + \text{length} + \text{width}
\]
Substituting the dimensions:
\[
P = 5 \, \text{cm} + 3 \, \text{cm} + 5 \, \text{cm} + 3 \, \text{cm} = 16 \, \text{cm}
\]
### Which Strategy is More Efficient?
The first method, using the perimeter formula, is generally more efficient. It succinctly calculates the perimeter in one step and requires less arithmetic. The second method, while valid, involves more additions and may lead to more chances for error in calculations. Thus, using the formula is often quicker and simpler.