Question

The perimeter of a rhombus is 160 cm and one diagonal is 10 cm long, then length of the other diagonal is

• A. $\sqrt{10}$ cm
• B. $30\sqrt{7}$ cm
• C. $30\sqrt{10}$ cm
• D. $\sqrt{2400}$

Answer 1

The correct option is B $30\sqrt{7}$ cm

"Given that Perimeter of rhombus $ABCD=160$cm $\Rightarrow 4\times$ side $=160\Rightarrow$ side $=40$cm
Since all sides of a rhombus are equal, so, $AB=BC=CD=DA=40$cm
Now, diagonal $AC=10$cm
As we know that the diagonals of a rhombus bisect each other at ${90}^0$, so $AO=OC=5$cm
In $△AOB$, $AO=5$cm and $AB=40$cm.
By Pythagoras theorem, $A{B}^2=A{O}^2+O{B}^2$$So,{40}^2=5^2+O{B}^2$
On solving we get, $O{B}^2=1575\Rightarrow OB=15\sqrt{7}\Rightarrow BD=2\times OB\Rightarrow BD=30\sqrt{7}$
So, the second diagonal is of length $30\sqrt{7}$ cm