Question

If $x$ and $y$ are respectively the areas of a square and a rhombus of sides of same length, then what is $x:y$?

• A. $1:1$
• B. $2:\sqrt{3}$
• C. $4:\sqrt{3}$
• D. $3:2$

Answer 1

The correct option is A $1:1$

R.E.F image

In $\Delta ABC$

$A{C}^2=x^2+x^2$

$\Rightarrow AC=\sqrt{2}x$

Similarly $BD=\sqrt{2}x$

$\frac{Areaofrhombus}{Areaofsquare}=\frac{\frac{AC\times BD}{2}}{x^2}=\frac{x^2}{x^2}=1$