Question

The lengths of the diagonals of a rhombus are $40cm$ and $42cm.$ Find the length of each side of the rhombus.

Answer 1

Let $ABCD$ be a rhombus with $AC$ and $BD$ as its diagonals.
We know that the diagonals of a rhombus bisect each other at right angles.
Let $O$ be the intersecting point of both the diagonals.
Let $AC=42cm$ and $BD=40cm$

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

$OA=\frac{42}{2}=21cm$

$OB=\frac{BD}{2}$

$OB=\frac{40}{2}=20cm$

In right angled triangle $\Delta AOB$, by Pythagoras theorem, we have
$A{B}^2=O{A}^2+O{B}^2$

$=(21{)}^2+(20{)}^2$

$=441+400$

$=841$
$\therefore AB=\sqrt{841}=\sqrt{29\times 29}=29cm$
Hence, each side of the rhombus is of length $29cm$