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When all of the linear dimensions are doubled . . .-- the perimeter is also doubled-- the area is multiplied by 22 = 4.
When the linear dimensions of a plane figure are quadrupled, its perimeter is quadrupled, and its area is multiplied by 42 = 16 .
Linear units are used for perimeter because perimeter measures the total length around a shape, which is a one-dimensional measurement. In contrast, area measures the extent of a surface in two dimensions, requiring the multiplication of two linear measurements (length and width), resulting in square units. This distinction helps accurately represent the different dimensions involved in each measurement.
Area is quadrupled (*4) and perimeter is doubled.
A perimeter is a linear measurement. An area is the product of two linear measurements, such as length and width. I cannot imagine what you mean by "perimeter area."