Question

If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus respectively?

• A. 1 : 1
• B. 3 : 4
• C. More than 1
• D. 1 : 1

Answer 1

The correct option is D (More than $1$)

Let the side of square be $a$ units then
Area of square = $a^2$ where $a$ is base length
Area of rhombus with same base $=a\times h$
where $h$ is perpendicular height.

Thus, the ratio of area of square to area of rhombus $=\frac{a^2}{ah}$
$=\frac{a}{h}$....(i)
From the right angled triangle $\Delta BCE$, where height($CB=h$)$<$ Hypotenuse$(BE=a)$
$\Rightarrow h<a$
$\Rightarrow \frac{a}{h}>1$
Thus, from equation(i), the ratio of area of square to area of rhombus is more than $1$