Question

The lengths of the diagonals of a rhombus are 24 cm and 32 cm The perimeter of the rhombus is

• A. 49 cm
• B. 128 cm
• C. 80 cm
• D. 56 cm

Answer 1

The correct option is C 80 cm

Perimeter of rhombus$=4\times a$

Where 'a' is the side of rhombus

$a=\sqrt{{\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2}$

Where $d_1$ and $d_2$ are digonals

Given $d_1=32cm$ and $d_2=24cm$

$\therefore a=\sqrt{{\left(\frac{32}{2}\right)}^2+{\left(\frac{24}{2}\right)}^2}$

$\Rightarrow a=\sqrt{(12{)}^2+(16{)}^2}$

$\Rightarrow a=\sqrt{144+256}$

$\Rightarrow a=\sqrt{400}$

$\Rightarrow a=20cm$

Hence perimeter of rhombus$=4\times 20=80cm$