Question

The perimeter of a rhombus is 40 cm. If one diagnonal is 16 cm. find :

(i) its another diagonal (ii) area

Answer 1

(i)Perimeter of rhombus =40 cm

$\therefore$ side $=\frac{1}{4}\times 40$

=10 cm One diagonal =16 cm

$\because$ Diagonals of rhombus bisect each other at right angles.

$OB=\sqrt{A{B}^2-O{A}^2}$

$=\sqrt{(10{)}^2-(8{)}^2}$

$=\sqrt{100-64}$

$=\sqrt{36}$ =6 cm

$\therefore$ diagonal BD $=6\times 2=12cm$

(ii)Area of rhombus

$=\frac{1}{2}\times$ product of diagonals

$=\frac{1}{2}\times 12\times 16$

$=96c{m}^2$

$\therefore \left(i\right)12cm\left(ii\right)96c{m}^2$