Question

The diagonals of two squares are in the ratio of 2:5.Find the ratio of their areas?

Answer 1

let diagonal 1st sqre=2x
√2(side)=2x
side=2x/√2
side=√2x
area of 1st square=(√2x)(√2x)
= 2x^2
let side of 1nd square=5x
side=5x/√2
area=25x^2/2
ratio of area s=2x^2 : 25x^2/2
= 2 : 25/2
=4 : 25

Answer 2

Area of a square = 1/2 * d² ( diagonal )

Let the diagonal of first square be 2x and another be 5x,

Area of 1st square = 1/2*(2x)² = 1/2*(4x²)

area of 2nd square = 1/2*(5x)² = 1/2 *(25x²)

Ratio of areas = [ 1/2*(4x²) ] : [ 1/2*(25x²) ]

=> 4 : 25,

Therefore the ratio of the areas of two squares is 4:25,

Hope you understand ,

Have a great day!!