Question
The length of a frame is 3 inches longer than 2 times the width. Which of the following equations describes the relationship between the width (w) of the frame in inches, and the area (A) in square inches? 2w+3
A. A = 2w + 3
B. A = 2w^2 + 3w
C. A = 2 (w^2 + 3)
D. A = 6w^2
A. A = 2w + 3
B. A = 2w^2 + 3w
C. A = 2 (w^2 + 3)
D. A = 6w^2
Answers
GPT-4o mini
To establish the relationship between the width \( w \) and the area \( A \) of the frame, we first need to set up the equations based on the information given.
We know that the length \( l \) of the frame is 3 inches longer than 2 times the width \( w \). This can be expressed as:
\[
l = 2w + 3
\]
The area \( A \) of the rectangle (frame) is given by the formula:
\[
A = l \times w
\]
Substituting the expression we found for the length into the area formula gives:
\[
A = (2w + 3) \times w
\]
Now we can distribute \( w \):
\[
A = 2w^2 + 3w
\]
Therefore, the equation that describes the relationship between the width \( w \) and the area \( A \) in square inches is:
\[
A = 2w^2 + 3w
\]
Looking at the provided options, the correct answer is:
**B. A = 2w^2 + 3w**
We know that the length \( l \) of the frame is 3 inches longer than 2 times the width \( w \). This can be expressed as:
\[
l = 2w + 3
\]
The area \( A \) of the rectangle (frame) is given by the formula:
\[
A = l \times w
\]
Substituting the expression we found for the length into the area formula gives:
\[
A = (2w + 3) \times w
\]
Now we can distribute \( w \):
\[
A = 2w^2 + 3w
\]
Therefore, the equation that describes the relationship between the width \( w \) and the area \( A \) in square inches is:
\[
A = 2w^2 + 3w
\]
Looking at the provided options, the correct answer is:
**B. A = 2w^2 + 3w**