Question

if the perimeter of two squares are in the ratio a : b, prove that their areas are in the
ratio a?:b?.
​

Answer 1

Answer:

Let

Perimeter ratio is a:b

And ratio of perimeters of squares are 4x:4y

So. X:Y

Simillarly

Area is. Xsqaure:Ysquare

By adding square root on both sides. It's X:Y

Step-by-step explanation:

Given

Perimeter ratio is a:b

And ratio of perimeters of squares are 4x:4y

So. X:Y

Simillarly

Area is. Xsqaure:Ysquare

By adding square root on both sides. It's X:Y

Therefore perimeter ratio is a:b

Whereas areas ratio is also a:b

Answer 2

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.