Question

the area of a square and that of a square drawn on its diagonals are in the ratio

Answer 1

$let \: side \: of \: square \: = x \\ diagonal \: of \: square \: = x \sqrt{2} \\ a1 = {x}^{2} \\ a2 = {(x \sqrt{2)} }^{2} = 2 {x}^{2} \\ \frac{a1}{a2} = \frac{ {x}^{2} }{2 {x}^{2} } = \frac{1}{2}$

Answer 2

1:2

Step-by-step explanation:

Let the side of the square be a

As we know,

Area of a square = side^2

= a^2

Now,

The length of the diagonal would be $\sqrt{2}$a           (∵ Pythagoras theorem)

Thus,

The ratio of the area of a square and of a square drawn on its diagonals

$= a^2/(\sqrt{2} a)^2$

= $a^2/2a^2$

= 1/2

∵ 1:2 is the ratio.

Learn more: Find the ratio

brainly.in/question/40683559