Question

the diagonals of two squares are in the ratio of 3:7 . find the ratio of their areas ? ​

Answer 1

Step-by-step explanation:

Let the two square be ; square 1 and square 2

Now,

let the diagonal of square 1 be D1 and the diagonal of square 2 be D2

Then,

According to the question,

The diagonals of two squares are in ratio 2:5

= D1 : D2 = 2:5

D1/D2=2/5_____(1)

also,

we know that ,

Area of a square = (1/2) (diagonal)^2

now,

let the area of square 1 be A1 and the area of square 2 be A2

Then,

A1=(1/2)(D1)^2____(2)

and A2=(1/2)(D2)^2____(3)

Now,

dividing eg -(2) by eg -(3)

we get,

=(A1/A2) =(D1^2/(D2)^2

=A1/A2=(2/5)^2. (using eg - (1)

=A1/A2=4/25

A1:A2=4/25

Thus , the required ratio of the areas of the two squares is 4:25