Question

The diagonals of a rhombus are in the ratio 2:3 and the area is 27 $c{m}^2,$ then find the lengths of the diagonals of a rhombus.

• A. $6cm,9cm$
• B. $7cm,8cm$
• C. $8cm,9cm$
• D. $7cm,6cm$

Answer 1

The correct option is A $6cm,9cm$

Given that diagonal of rhombus are in the ratio $2:3$ and area is $27$ $c{m}^2$

Let the diagonal of rhombus are $2x$ and $3x$

Then area=$\frac{d_1\times d_2}{2}=\frac{2x\times 3x}{2}=3x^2$ $c{m}^2$

But area is $27$ $c{m}^2$

$\therefore 3x^2=27\Rightarrow x^2=9\Rightarrow x=3$

Then diagonals are $2\times 3=6$ $cm$ and $3\times 3=9$ $cm$