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A rectangle has sides that measure**

[12x + 8] units long and [8x + 5] units long. What are the expressions that represent the perimeter and area of the rectangle?
A. Perimeter: [40x + 18] units, Area: [96x² + 100x + 40] square units
B. Perimeter: [32x + 13] units, Area: [96x² + 100x + 40] square units
C. Perimeter: [40x + 18] units, Area: [96x² + 69x + 40] square units
D. Perimeter: [32x + 13] units, Area: [96x² + 69x + 40] square units

User Anayka
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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.

User Zyamys
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