Question

The side of a rhombus is $10cm$ and the length of one of the diagonals is $12cm$. Find the length of the other diagonal

Answer 1

Diagonals of rhombus bisect each other at right angles.

Let $ABCD$ be the rhombus, diagonal $AC=12cm$ and $AB=10cm$

In $△AOB,AB=10cm,AO=8cm$

$\Rightarrow$ $(AB{)}^2=(AO{)}^2+(BO{)}^2$ [ By Pythagoras theorem ]

$\Rightarrow$ $(10{)}^2=(6{)}^2+(BO{)}^2$

$\Rightarrow$ $100=36+(BO{)}^2$

$\Rightarrow$ $(BO{)}^2=64$

$\therefore$ $BO=8cm$

$\therefore$ Diagonal $BD=2\times 8=16cm$