Question

Calculate the perimeters of the original figure (not including the eyes) and the scale drawing. Write a statement comparing the perimeters. Original: 16

a) Perimeter of the original figure: 16; Perimeter of the scale drawing: 8; The scale drawing is half the size of the original.
b) Perimeter of the original figure: 16; Perimeter of the scale drawing: 32; The scale drawing is twice the size of the original.
c) Perimeter of the original figure: 8; Perimeter of the scale drawing: 16; The scale drawing is half the size of the original.
d) Perimeter of the original figure: 8; Perimeter of the scale drawing: 16; The scale drawing is the same size as the original.

Answer 1

The perimeter of the original figure is 16 units. The perimeter of the larger scale drawing, which is scaled up by a factor of 2, is 32 units. Hence, the scale drawing's perimeter is twice the size of the original's perimeter.

Step-by-step explanation:

To calculate the perimeters of both the original figure and the scale drawing, we need to understand that the scale drawing's dimensions are directly related to the original figure by a constant called the scale factor. As you've stated, the side length of the larger square (which we can consider to be the scale drawing) is calculated by doubling (scale factor of 2) the side length of the original figure.

The original figure has a perimeter of 16 units. If each side of the original square is 's' units, then 4s = 16, which means each side is 4 units long. When the dimensions are scaled up by a factor of 2, the side length becomes 4 x 2 = 8 units for the scale drawing. Thus, the perimeter of the scale drawing will be 4 sides × 8 units/side = 32 units.

Therefore, the correct statement comparing the perimeters is: Perimeter of the original figure: 16; Perimeter of the scale drawing: 32; The scale drawing is twice the size of the original. This aligns with option b.