Question

The perimeter of a rhombus is $60cm.$ If one of its diagonals is $18cm$ long, find (i) the length of the other diagonal, and (ii) the area of the rhombus.

Answer 1

Perimeter of Rhombus $=4\times$Side $=60cm$

Side $=\frac{60}{4}=15cm$

Now, the Diagonals of a rhombus bisect each other at right angle.

So, OC $=\frac{1}{2}\times AC=9cm$

In triangle DOC, we have

$\Rightarrow C{D}^2=O{D}^2+O{C}^2$

$\Rightarrow {15}^2=O{D}^2+9^2$

$\Rightarrow O{D}^2=225-91=144$

$\Rightarrow OD=12cm$

So, $BD=2\times OD=2\times 12=24cm$

Now, Area of the rhombus ABCD $=\frac{1}{2}\times d_1\times d_2=\frac{1}{2}\times 24\times 18=432=216c{m}^2$