Two rectangles are similar and the ratio of their sides is 1: 4. Find the ratio of their perimeters??? Find the ratio of their areas??? How do I do this?
To find the ratio of the perimeters of two similar rectangles, you need to understand that the perimeter of a rectangle is equal to the sum of all its sides.
Given that the rectangles are similar and the ratio of their sides is 1:4, let's denote the length of the sides of the first rectangle as 1x and the length of the sides of the second rectangle as 4x.
The perimeter of the first rectangle would then be 2(1x + 4x) = 10x, and the perimeter of the second rectangle would be 2(4x + 16x) = 40x.
Hence, the ratio of their perimeters is 10x:40x, which simplifies to 1:4.
Now, to find the ratio of their areas, we need to understand that the area of a rectangle is calculated by multiplying its length and width.
The area of the first rectangle would be (1x) * (4x) = 4x^2, and the area of the second rectangle would be (4x) * (16x) = 64x^2.
Hence, the ratio of their areas is 4x^2:64x^2, which simplifies to 1:16.
Therefore, the ratio of their perimeters is 1:4, while the ratio of their areas is 1:16.