Question

if the ratio of the areas of two squares is a :b then the ratio of their sides ,ratio of their perimeters and ratio of the diagonals will be
a)a:b
b)a^2:b^2
c)√a:√b
d) none
​

Answer 1

Step-by-step explanation:

iven, ratio of areas of square =  

1

9

​  

 

we know that,

Area of square =a  

2

 

perimeter of square =1a

where  

′

a  

′

 is any side of square.

Area of square(A  

2

​  

)

Area of square(A  

1

​  

)

​  

=  

a  

2

2

​  

 

a  

1

2

​  

 

​  

=  

1

9

​  

 

a  

2

​  

 

a  

1

​  

 

​  

=  

1

9

​  

 

​  

 

a  

2

​  

 

a  

1

​  

 

​  

=  

1

3

​  

 

∴  

Perimeter of square.(2)

Perimeter of square.(1)

​  

=  

4a  

2

​  

 

4a  

1

​  

 

​  

=  

4

4

​  

×(  

1

3

​  

)

Perimeter of square.(2)

Perimeter of square.(1)

​  

=  

1

3

​