Final answer:
The perimeter of the rectangle is 40x + 26 units, and the area is 96x² + 124x + 40 square units. These expressions are obtained by using the formulas for the perimeter (P = 2(length + width)) and area (A = length × width) of a rectangle, which do not match the given options.
Step-by-step explanation:
To find the expressions that represent the perimeter and area of the rectangle with sides measuring [12x + 8] units and [8x + 5] units, we apply the perimeter and area formulas for rectangles.
Perimeter of a Rectangle
The perimeter (P) of a rectangle is found by adding the lengths of all four sides. Since a rectangle has opposite sides of equal length, the formula is P = 2(length + width). Substituting the given expressions for length and width:
P = 2[(12x + 8) + (8x + 5)]
P = 2[12x + 8x + 8 + 5]
P = 2[20x + 13]
P = 40x + 26
Area of a Rectangle
The area (A) of a rectangle is found by multiplying the length by the width. Using the given expressions:
A = (12x + 8)(8x + 5)
A = 96x² + 60x + 64x + 40
A = 96x² + 124x + 40 square units
Therefore, the correct expressions for the perimeter and area of the rectangle are Perimeter: [40x + 26] units and Area: [96x² + 124x + 40] square units, which does not match any of the given options A, B, C, or D.