Suryateja R. answered • 04/17/20
Medical Student/Johns Hopkins Alum and Admissions Counselor
The ratio of perimeters of the similar figures will be equivalent to the scale factor of the given dimension between the two similar figures. For example, if 2 squares are given, 1 with a side length of 1 and the other with a side length of 2, the scale factor will be 2. Therefore, the perimeters of figure A (1) and figure B (2) will be 1:2.
The ratio of areas of similar figures will be equivalent to the square of the scale factor of the given dimension between the two figures, because the calculation of area always involves taking the square of a dimension of the figure. For example, if two squares are given, one with l=1, one with l=2, the scale factor is 2. Since area is calculated as l^2, or l^2, the ration will be the square of the scale factor: 2^2, which is 4. Therefore, the areas of the similar squares of these dimensions will be in the ratio is 1:4.
General formulas:
Similar figures, l1 = n, l2=m
Scale factor s=m/n
Perimeter ratio: 1:s
Area ratio: 1:s^2
