Answer:
If we have two figures, F and F'
Such that if we start with F, and dilate it with a scale factor K, we get F'.
We will have:
All the measures of F', are K times the correspondent measures of F.
Then if F has s₁, s₂, ..., sₙ sides, the sides of F' will be:
K*s₁, K*s₂, ..., K*sₙ
The ratio between correspondent sides will be equal to K
The ratio between perimeters will also be equal to K (because the perimeter is the sum of all the sides of each figure, so we can just take K as a common factor)
In the case of the area, because we usually multiply a measure by another, a factor K^2 will appear, and the quotient between the areas is K^2
And finally, for the volumes, the ratio will be K^3
a) The ratio of corresponding lengths is K, in this case is 5/2
b) The ratio of the perimeters is K, in this case is 5/2
c) The ratio of the areas is K^2, in this case is (5/2)^2 = 25/4
d) The ratio of the areas is K^3, in this case is (5/2)^3 = 125/8
e) Two figures are similar if the figures have the same shape, then the corresponding angles are exactly the same, then the ratio of corresponding angle measures is 1.
