Question

In general, if the ratio between the sides of two figures is a : b , suggest a general rule for the relationships between

1. the ratio of the sides and the ratio of their perimeters
2. the ratio of the sides and the ratio of their areas.

Answer 1

Let it be 2 squres of side a and b
Perimeter of squre with side a=4a
Perimeter of second square =4b
So ratio of perimeters=4a/4b=a/b
So it is same as the ratio of sides

Area of 1st squre=a*a
Second squre=b*b
So ratio of areas=a^2/b^2
so ratio of areas is the squre of ratio of sides

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