Question

A diagonal of a rhombus is 80% of the other diagonal. Then area of the rhombus is how many times the square of the longer diagonal?

• A. $\frac{2}{5}$
• B. $\frac{4}{5}$
• C. $\frac{3}{4}$
• D. $\frac{1}{4}$

Answer 1

Answer: (A)

$\frac{2}{5}$

Let $x$ be the shorter diagonal and $y$ be the longer diagonal of a rhombus.
$\therefore$ Area of Rhombus$=$$\frac{xy}{2}$$uni{t}^2$
But, $x=80\%y$
$\therefore$Area of Rhombus$=\frac{80}{2\left(100\right)}{y}^2$$uni{t}^2$
$\therefore$Area of Rhombus$=\frac{2}{5}{y}^2$$uni{t}^2$
$\therefore$Area of Rhombus is $\frac{2}{5}$ times the square of the longer diagonal.