Question

The ratio of the area of a square to that of the square drawn on its diagonal is $1:2$
If true then enter $1$ and if false then enter $0$

Answer 1

Let the side of a square be $a$.

Area of square$\left(S_1\right)=a^2$

Length of the diagonal $=\sqrt{a^2+a^2}=a\sqrt{2}$

Now draw a square on its diagonal where length of each sides is $a\sqrt{2}$

Area of a square formed on diagonal of first square is $\left(S_2\right)=(a\sqrt{2}{)}^2=2a^2$

Then $\frac{S_1}{S_2}=\frac{a^2}{2a^2}=\frac{1}{2}$

Thus, $S_1:S_2=1:2$

Hence, the correct answer is $1$.