Answer:
[tex] {x}^{2} + 3x[/tex]
Step-by-step explanation:
1.
Area of shaded region = Area of external rectangle - Area of internal rectangle
[tex] = 4x(x + 2) - x(3x + 5) \\ = 4 {x}^{2} + 8x - 3 {x}^{2} - 5x \\ = 4 {x}^{2} - 3 {x}^{2} + 8x - 5x \\ = {x}^{2} + 3x \\ [/tex]
2.
Let the width of the rectangle be x inches.
Therefore, length of the rectangle = (x + 3) inches
A.
Area of rectangle
[tex] =(x + 3)\times x\\
=x^2 + 3x\\[/tex]
B.
Width of rectangle = 4 inches
Length of rectangle = 4 + 3 = 7 inches
Area of rectangle = 7*4 = 28 square inches.
