The figures are similar. The ratio of the lengths of their corresponding sides is 45:25, or 9:5. Find the ratio of their perimeters and the ratio of their areas. The figures are not drawn to scale.

perimeter of two figures = 9 : 5

area of the two figures = 9^2 : 5^2
= 81 : 25

To find the ratio of the perimeters, we need to compare the sum of the lengths of corresponding sides.

Let's assume the lengths of the sides of the first figure are 9x and 5x, where x is some positive value. Similarly, the lengths of the sides of the second figure would be 45x and 25x in order to maintain the 9:5 ratio.

The ratio of the perimeters would be:
(9x + 5x) : (45x + 25x)
= 14x : 70x
= 1:5

Therefore, the ratio of their perimeters is 1:5.

To find the ratio of their areas, we need to compare the squares of the lengths of corresponding sides.

The area of the first figure would be (9x)^2, and the area of the second figure would be (45x)^2 since the ratio of lengths is 9:45, or 1:5.

The ratio of the areas would be:
(9x)^2 : (45x)^2
= 81x^2 : 2025x^2
= 1:25

Therefore, the ratio of their areas is 1:25.

To find the ratio of the perimeters, we can use the fact that similar figures have proportional side lengths.

Given that the ratio of the lengths of their corresponding sides is 9:5, let's assume the first figure has side lengths 9x and the second figure has side lengths 5x.

To find the ratio of their perimeters, we need to add up all the side lengths for each figure.

The first figure's perimeter is 4 * (9x) = 36x.
The second figure's perimeter is 4 * (5x) = 20x.

Therefore, the ratio of their perimeters is 36x:20x, which simplifies to 9:5.

Now let's move on to finding the ratio of their areas.

We know that the ratio of the lengths of their corresponding sides is 9:5.

Since the area of a figure is proportional to the square of its side length, we can square the ratio 9:5 to find the ratio of their areas.

(9:5)^2 = 81:25

Thus, the ratio of their areas is 81:25.

To summarize:
- The ratio of their perimeters is 9:5.
- The ratio of their areas is 81:25.