Question

The diagonals of a rhombus are in the ratio 2:3. Find the length of smaller diagonal, if the area of the rhombus is 27 $c{m}^2.$

Answer 1

Given
Ratio of the diagonals = 2:3
Area of the rhombus = 27 cm${}^2$

Let the length of the smaller diagonal be 2y and the larger diagonal be 3y

Area of the rhombus
$=\frac{1}{2}\times$(product of diagonals)

$27=\frac{1}{2}\times 2y\times 3y$

$27=\frac{1}{2}\times 6y^2$

$27=3y^2$

$\Rightarrow y^2=\frac{27}{3}=9$

y = $\sqrt{9}$ = 3

Hence, length of the smaller diagonal = 2y = 2(3) = 6 cm