Question

if length of a diagnol of a rhombus is 30 cm and its area is 240sq cm find its perimeter
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Answer 1

$\Large\underline{\underline{\sf \green{Given}:}}$

• Lenght of diagonal of Rhombus = 30cm

• Area of Rhombus (A) = 240cm²

$\Large\underline{\underline{\sf \green{To\:Find}:}}$

• Perimeter of all sides (P) = ?

$\Large\underline{\underline{\sf \green{Formula\:Used}:}}$

$\large{\boxed{\sf \red{Area\:Of\: Rhombus (A)=\dfrac{1}{2}×d_1×d_2}}}$

$\large{\boxed{\sf \red{Perimeter\:Of\: Rhombus (P)=sum\:of\:all\:sides}}}$

$\Large\underline{\underline{\sf \green{Solution}:}}$

$\implies{\sf A=\dfrac{1}{2}×d_1d_2}$

$\implies{\sf 240=\dfrac{1}{2}×30×d_2 }$

$\implies{\sf d_2=16\:cm}$

$\implies{\sf side\:of\:Rhombus=\sqrt{\left(\dfrac{30}{2}\right)^2+\left(\dfrac{16}{2}\right)^2} }$

$\implies{\sf \sqrt{15^2+8^2} }$

$\implies{\sf 17\:cm }$

$\large{\sf Perimeter\:of\: Rhombus=sum\:of\:all\:sides}$

$\implies{\sf 4×17 }$

$\implies{\sf 68\:cm }$

$\Large\underline{\underline{\sf \green{Answer}:}}$

⛬ Perimeter of Rhombus is 68 cm .