Question

If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is equal to when one angle of rhombus is of ${30}^{\circ }$

• A. $2$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $2$

Let ${}^{\prime }{a}^{\prime }$ be the base of square and rhombus.

Now, in $△EDG$,

$Sin{30}^0=\frac{h}{a}$

$\frac{1}{2}=\frac{h}{a}$

$h=a/2$

Area of square $=a^2$

Area of rhombus $=$ base $\times$ height

$=a\times \frac{a}{2}$

$=a^2/2$

$\frac{Areaofsquare}{Areaofrhombus}=\frac{a^2}{a^2/2}=\frac{2}{1}$