The area of a rhombus is 480 cm2, and one of its diagonals measures 48 cm.

Solution:

i) Area of a rhombus $=\frac{1}{2} \times d_{1} \times d_{2}$, where $d_{1}$ and $d_{2}$ are the lengths of the diagonals.

$\Rightarrow 480=\frac{1}{2} \times 48 \times d_{2}$

$\Rightarrow d_{2}=\frac{480 \times 2}{48}$

$\Rightarrow d_{2}=20 \mathrm{~cm}$

∴ Length of the other diagonal = 20 cm

(ii) Side $=\frac{1}{2} \sqrt{d_{1}^{2}+d_{2}^{2}}$

$=\frac{1}{2} \sqrt{48^{2}+20^{2}}$

$=\frac{1}{2} \sqrt{2304+400}$

$=\frac{1}{2} \sqrt{2704}$

$=\frac{1}{2} \times 52$

 

$=26 \mathrm{~cm}$

∴ Length of the side of the rhombus = 26 cm

(iii) Perimeter of the rhombus $=4 \times$ Side

$=4 \times 26$

$=104 \mathrm{~cm}$