If the diagonals of two squares are in the ratio of 3 : 5, then their areas will be in the ratio of :

Correct option is A

Given:

The diagonals of two squares are in the ratio of 3 : 5

Formula used:

The area A  of a square can be expressed in terms of its diagonal  d using the formula: 

A = $$\frac{1}{2}\times d^2$$

Solution:

The diagonals of the two squares are in the ratio 3:5 

Diagonal of the first square: $$d_1 = 3x$$ 

​Diagonal of the second square $$d_2$$ = 5x 

​Area of the first square:

$$A_1 = \frac{1}{2}(d_1)^2=\frac{1}{2}(3x)^2= \frac{1}{2}.9x^2= \frac{9}{2}x^2$$ 

​Area of the second square:

​$$A_2 = \frac{1}{2}(d_2)^2=\frac{1}{2}(5x)^2= \frac{1}{2}.25x^2= \frac{25}{2}x^2$$ 

Ratio of areas = $$\frac{A_1}{A_2}$$ = $$\frac{\frac{9}{2}x^2}{\frac{25}{2}x^2}$$​

Ratio of areas = $$\frac{9}{25}$$ 

​Thus, the ratio of the areas of the two squares is 9:25​