We are given that the length of a rectangle is 3 inches greater than the width.
Let us draw a rectangle and label the width and length.
Part A:
Let the width of the rectangle is x inches.
Then the length of the rectangle is (x + 3) inches.
Now recall that the area of a rectangle is given by
[tex]A=L\cdot W[/tex]Where L is the length and W is the width of the rectangle.
[tex]\begin{gathered} A=(x+3)\cdot x \\ A=x^2+3x \end{gathered}[/tex]Therefore, the above polynomial represents the area of the rectangle.
Part B:
We are given that the width is 4 inches.
Substitute the width (x = 4) into the equation of the area that we found in part A.
[tex]\begin{gathered} A=x^2+3x \\ A=(4)^2+3(4) \\ A=16+12 \\ A=28in^2 \end{gathered}[/tex]Therefore, the area of the rectangle is 28 square inches.
