Question

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

Answer 1

(i) Perimeter of Rhombus = 60 cm

$4\times$ Side = 60 cm

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

Now Diagonals of a Rhombus Bisect Each Other at right angle

$\frac{1}{2}\times 18=9cm$

Now Side Acts as a Hypotenuse

${\left(\frac{d}{2}\right)}^2={15}^2-9^2$

${\left(\frac{d}{2}\right)}^2=144$

Diagonal $=2\sqrt{144}=24$ cm

So Other Diagonal = 24 m

(ii) Now Area $=\frac{1}{2}\times d_1\times d_2$

$=\frac{1}{2}\times 24\times 18=216c{m}^2$