Question

Adjacent sides of a parallelogram are $11\text{cm}$ and $17\text{cm}$. If the length of one of its diagonal $26\text{cm}$, find the length of the other.

Answer 1

Let $ABCD$ be a parallelogram.
$\therefore AB=17cm,BC=11cm$ and $AC=26cm$
Let its diagonal $AC$ and $BD$ bisect each other at point $O$.
$AO=\frac{1}{2}\times AC$
$=\frac{1}{2}\times 26$
$=13cm$
and $BO=\frac{1}{2}BD$
In $\Delta ABC$, $BO$ is a median.
$\therefore (AB{)}^2+(BC{)}^2=2(BO{)}^2+2(AO{)}^2$ (by Apollonius theorem)
$(17{)}^2+(11{)}^2=2B{O}^2+2(13{)}^2$
$289+121=2B{O}^2+338$
$2B{O}^2=72$
$B{O}^2=\frac{72}{2}=36$
$BO=\sqrt{36}$
$=6cm$

$\therefore$ length of diagonal $=2\times 6=12cm$