Question

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

• A. $\sqrt{10}cm$
• B. $\sqrt{37}cm$
• C. $6\sqrt{15}cm$
• D. $\sqrt{41}cm$

Answer 1

The correct option is C $6\sqrt{15}cm$

Given that perimeter of rhombus$=160cm$ and one diagonal$=10cm$ ,

We know that perimeter of the rhombus $=4a$

$4a=160$

$a=160/4=40cm$

Therefore Each side of the rhombus $=40cm$.

Length of the one diagonal $=10cm$.

Then the length of the other diagonal will be:

$=2\times \sqrt{{40}^2-{\left(\frac{10}{2}\right)}^2}$

$=2\sqrt{160-25}$

$=2\sqrt{135}=2\times 3\sqrt{15}=6\sqrt{15}cm$

Hence, this is the answer.