Often when working a problem with a scale factor, you are given two similar shapes, and a missing side. For example, you could be given a rectangle with sides A: 3 units and side B: 9 units. Then, you are given another similar rectangle, with side A: 6 units and side B: unknown. To solve this problem, you can simply create a proportion, known in this case as a scale factor.
Similar to using a map to predict travel times on a road trip, you can simply create a proportion, in this case, 6:3, which simplifies to 2:1. In this case, the scale factor is 2, so the length of a similar side in the 1st shape is multiplied by 2 to get the length of the same side in the other (2nd) shape. Knowing this side is 9 in the first, and the scale factor is two, we know that the similar side in the 2nd shape is going to be 9 x 2 = 18 units long.
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if the length and breadth are increased by 5 times each area becomes 25 times
You increase the scale factor.
The area scale factor is the square of the side length scale factor.
If you know the perimeter, there is no need to find it again.