The perimeter of a rhombus is 60 cm.


The perimeter of a rhombus is 60 cm. If one of its diagonals is 18 cm long,


(i) the length of the other diagonal, and

(ii) the area of the rhombus.



Perimeter of a rhombus = 4a    (Here, a is the side of the rhombus.)

$\Rightarrow 60=4 a$


$\Rightarrow a=15 \mathrm{~cm}$

(i) Given:
One of the diagonals is 18 cm long.

$d_{1}=18 \mathrm{~cm}$

Thus, we have:

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

$\Rightarrow 15=\frac{1}{2} \sqrt{18^{2}+d_{2}^{2}}$

$\Rightarrow 30=\sqrt{18^{2}+d_{2}^{2}}$

Squaring both sides, we get:

$\Rightarrow 900=18^{2}+d_{2}^{2}$

$\Rightarrow 900=324+d_{2}^{2}$

$\Rightarrow d_{2}^{2}=576$


$\Rightarrow d_{2}=24 \mathrm{~cm}$

∴ Length of the other diagonal = 24 cm

(ii) Area of the rhombus $=\frac{1}{2} d_{1} \times d_{2}$

$=\frac{1}{2} \times 18 \times 24$

$=216 \mathrm{~cm}^{2}$


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