Question

If the perimeters of two squares are in the ratio a : b, prove that their areas are in the ratio a^ : b^.​

Answer 1

Answer:

let the sides of the squares be x and y units, where x > y.

ATQ

ratio of their perimeters = a/b

4x/4y = a/b

x/y = a/b ------ (i)

now,

ratio of areas = x^2/y^2

                       = (x/y)^2

                       = (a/b)^2 [ from eq (i)]

                       = a^2 : b^2

hence proved.

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