Question

$ABCD$ is a parallelogram whose diagonals intersects each other at right angles if the length of the diagonals are $16$ centimetre and $12$ centimetre find the length of all sides and its perimeter

Answer 1

Let $AC$ and $BD$ are the diagonal of the parallelogram.

Here, $AC=12$ cm, $BD=16$ cm

Now, $AC$ and $BD$ bisect each other ate right angle at the point $O$.

Now,$OB=\frac{BD}{2}=\frac{16}{2}=8$

$OA=\frac{AC}{2}=\frac{12}{2}=6$

and $\angle AOB={90}^{\circ }$

From $△AOB$

Using Pythagoras theorem, ${AB}^2={OB}^2+{OA}^2$

$\Rightarrow {AB}^2=8^2+6^2=64+36=100$

$\therefore AB=10$cm

By the property of Rhombus, all its sides are equal.

Hence $BC=CD=AD=AB=10$cm

$\therefore ,$Perimeter$2(10+10)=2\times 20=40$cm