The diagram shows corresponding lengths in two similar figures find the ratio of the perimeters and the ratio of the areas

The ratio of the perimeters is the same as the ratio of the side lengths.
The ratio of the areas is the square of the ratio of the side lengths.

For example, you have two similar rectangles.
One has a side of 4 m, and the other one has a corresponding side of 12 m.
The ratio of the side lengths is 12/4 = 3.
All sides of the second one are 3 times longer than the corresponding sides of the first one. Also the perimeter of the second one is 3 tomes the perimeter of the first one.

For the areas, you must square the ratio. Since the ratio of side lengths is 3, square 3: 3^2 = 9. The area of the second one is 9 times the area of the first one.

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