Question

The perimeter of a rhombus is $96$ cm and obtuse angle of it is ${120}^o$. Find the lengths of its diagonals.

• A. $12\text{cm},12\sqrt{3}\text{cm}$
• B. $18\text{cm},18\sqrt{3}\text{cm}$
• C. $24\text{cm},24\sqrt{3}\text{cm}$
• D. $32\text{cm},32\sqrt{3}\text{cm}$

Answer 1

The correct option is C $24\text{cm},24\sqrt{3}\text{cm}$

Given,

Perimeter of rhombus=96

$4AB=96⟹AB=24cm$

As It is clearly see from the figure

In $\Delta AOB$

$sin60=\frac{BO}{AB},Cos60=\frac{OA}{AB}⟹\frac{\sqrt{3}}{2}=\frac{BO}{24},\frac{1}{2}=\frac{OA}{24}⟹OB=12\sqrt{3}cm,OA=12cm$

We get AC=2(OA) and BD=2(OB)

AC=24cm and BD=24$\sqrt{3}$cm