Question
A rectangle is 5 inches longer than it is wide. Which of the following polynomials represents the area of the rectangle?
Answers
GPT-4o mini
Let the width of the rectangle be denoted as \( w \). Since the rectangle is 5 inches longer than it is wide, the length \( l \) can be expressed as:
\[
l = w + 5
\]
The area \( A \) of a rectangle is given by the formula:
\[
A = l \times w
\]
Substituting the expression for the length into the area formula, we have:
\[
A = (w + 5) \times w
\]
Now, we can expand this expression:
\[
A = w^2 + 5w
\]
Thus, the polynomial representing the area of the rectangle is:
\[
w^2 + 5w
\]
\[
l = w + 5
\]
The area \( A \) of a rectangle is given by the formula:
\[
A = l \times w
\]
Substituting the expression for the length into the area formula, we have:
\[
A = (w + 5) \times w
\]
Now, we can expand this expression:
\[
A = w^2 + 5w
\]
Thus, the polynomial representing the area of the rectangle is:
\[
w^2 + 5w
\]