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=2w2+3w
cap A is equal to 2 w squared plus 3 w

A=2w+3

Answer 1

To find the equation that describes the relationship between the width (w) and the area (A) of the frame based on the information given, we start by expressing the length (L) in terms of the width (w).

According to the problem:

1. The length (L) is 3 inches longer than 2 times the width (w), which can be expressed as:
\[
L = 2w + 3
\]

2. The area (A) of the frame can be calculated using the formula:
\[
A = L \times w
\]

Substituting the expression for L into the area formula gives us:
\[
A = (2w + 3) \times w
\]

Now, distribute w:
\[
A = 2w^2 + 3w
\]

So the correct equation that describes the relationship is:
\[
A = 2w^2 + 3w
\]

This corresponds to the response:
**A=2w²+3w** (cap A is equal to 2 w squared plus 3 w).