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?(1 point) Responses A=6w2 cap A is equal to 6 w squared A=2(w2+3) cap A is equal to 2 times open paren w squared plus 3 close paren A=2w+3 cap A is equal to 2 w plus 3 A=2w2+3w
Answers
GPT-4o mini
To find the equation that describes the relationship between the width \( w \) of the frame and the area \( A \) of the frame, we first need to define the dimensions based on the information given.
Given:
- 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 a rectangle is calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for length \( l \) into the area formula:
\[
A = (2w + 3) \times w
\]
Expanding this:
\[
A = 2w^2 + 3w
\]
Now we can look for the equation that matches this expression from the given options.
The correct choice that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 2w^2 + 3w
\]
So, the option corresponding to this equation is:
**A = 2w² + 3w.**
Given:
- 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 a rectangle is calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for length \( l \) into the area formula:
\[
A = (2w + 3) \times w
\]
Expanding this:
\[
A = 2w^2 + 3w
\]
Now we can look for the equation that matches this expression from the given options.
The correct choice that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 2w^2 + 3w
\]
So, the option corresponding to this equation is:
**A = 2w² + 3w.**