The perimeter of a rectangle is represented by 4x + 24. In response to the question, "What is a possible representation of the area of this rectangle?" Mark says, &quo…

Question

The perimeter of a rectangle is represented by 4x + 24. In response to the question, "What is a possible representation of the area of this rectangle?" Mark says, "x² + 36,"and Sarah says, "No, x² + 12x +36." What assumptions are both Mark and Sarah making about the rectangle?

Answer 1

Both Mark and Sarah are making assumptions about the rectangle's dimensions based on the given representation of its perimeter.

Step-by-step explanation:

Both Mark and Sarah are making assumptions about the rectangle's dimensions based on the given representation of its perimeter, which is 4x + 24.

Mark assumes that one side of the rectangle is represented by x, and since the perimeter of a rectangle is twice the sum of its length and width, he uses the formula A = x * (4x + 24)/2, which simplifies to x² + 36 as a possible representation of the area.

Sarah assumes that both the length and width of the rectangle are represented by x, so she uses the formula A = x * x, which simplifies to x² + 12x + 36 as a possible representation of the area.