Question

The length of a side of a rhombus is $5m$ and one of its diagonals is length $8m$. The length of the other diagonal is

• A. $5m$
• B. $7m$
• C. $6m$
• D. $8m$

Answer 1

The correct option is C $6m$

Diagonals of rhombus are cut each other at ${90}^{\circ }$.
Since $d_1=8$ and $a=5$
Therefore, By Pythagoras theorem
$a^2={\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2$
$5^2=4^2+{\left(\frac{d_2}{2}\right)}^2$
$\Rightarrow {\left(\frac{d_2}{2}\right)}^2=25-16=9$
$\Rightarrow \frac{d_2}{2}=\sqrt{9}=3$
$\Rightarrow d_2=3\times 2=6$