Delhi Police Constable Exam Model Paper 1

GIVEN:
One of the diagonals of a rhombus is 18 cm and the area of the rhombus is 216 cm2
CONCEPT:
Diagonals of a rhombus bisect each other and are perpendicular to each other
FORMULA USED:
Area of rhombus = 1/2 × d1 × d2
d1 and d2 are the diagonals of rhombus.
CALCULATION:
Using the formula:
216 = 1/2 × 18 × d2
⇒ d2 = 24 cm
Now we know that the diagonals of a rhombus bisect each other and are perpendicular to each other

So, in triangle AOB:
$\mathit{A}{\mathit{B}}^2=\mathit{A}{\mathit{O}}^2+\mathit{B}{\mathit{O}}^2$
⇒ $\mathit{A}{\mathit{B}}^2=144+81$
⇒ $\mathit{A}{\mathit{B}}^2$ = 225
⇒ AB = 15 cm
∴ side of the rhombus = 15 cm∴ side of the rhombus = 15 cm