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Which expressions represent the large rectangle's total area?

A) 3(5 + b) and 5(b + 3)
B) 5b + 15 and 15 + 5b
C) 3.5 + 3b and 5(b + 3)
D) 5(b + 3) and 3.5 + 3b

1 Answer

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Final answer:

The total area of a large rectangle with sides 5 units and (3 units + variable b) is represented by the expressions 3(5 + b) and 5(b + 3).

Step-by-step explanation:

The student is asking which expressions represent the total area of a large rectangle. To find the area of a rectangle, we use the formula length multiplied by width. If we assume that one side of the rectangle is 5 units and the other side consists of a constant 3 units plus a variable b, then the expressions for the total area can be 5(b + 3) or 3(5 + b), since multiplication is commutative (A+B = B+A). Therefore, the correct expressions for the rectangle's total area are given by both A) 3(5 + b) and B) 5(b + 3), as they are simply rearrangements of the multiplication of the length and width of the rectangle.

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