Question

If perimeter of a rhombus is 100 cm and length of one diagonal is 48 cm, what is the area of the rhombus?

Answer 1

Perimeter of a rhombus = 100 cm (Given)

Let the diagonal AC= 48 cm

Let the side of the rhombus be x

Since there are 4 sides in a rhombus and all 4 are equal

4x = 100 cm

x = 25 cm


The triangle ABO is a right angle at O with AB being its hypotenuse.

$A{B}^2=B{O}^2+A{O}^2$

${25}^2={24}^2+B{O}^2$

$625=576+B{O}^2$

$625-576=B{O}^2$

$49=B{O}^2$

$7cm=BO$

Since the diagonals of a rhombus bisect each other, so length BD = 14 cm.

Area of rhombus $=\frac{1}{2}$ (Product of diagonals)

Area $=\frac{1}{2}\times 14\times 48$

=336 cm${}^2$