Question

The ares of a rhombus is $28c{m}^2$ and one of its diagonals is $4cm$. What is its perimeter?

• A. $4\sqrt{53}cm$
• B. $36cm$
• C. $2\sqrt{53}cm$
• D. $52cm$

Answer 1

The correct option is A $4\sqrt{53}cm$

$d_1=4cm,d_2=dcm$

Area of rhombus = ${28cm}^2$

$\frac{1}{2}\times d_1\times d_2=28\Rightarrow \frac{1}{2}\times 4\times d=28{cm}^2\Rightarrow d=14cm$

We know that diagonals of a rhombus bisect each other at right angle. Then in $△DOC$,

DC = $\sqrt{{\left(\frac{4}{2}\right)}^2+{\left(\frac{14}{2}\right)}^2}=\sqrt{4+49}=\sqrt{53}cm$

$\therefore$ Perimeter = $4\sqrt{53}cm$