Question

Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.

Answer 1

Diagonals of a rhombus bisect each other at right angles.
PR = 20 cm
$\Rightarrow \mathrm{PO}=\frac{1}{2}\mathrm{PR}=\frac{1}{2}\times 20=10\mathrm{cm}$
Similarly, QS = 48 cm
$\Rightarrow \mathrm{QO}=\frac{1}{2}\mathrm{SQ}=\frac{1}{2}\times 48=24\mathrm{cm}$
In $△$POQ, applying Pythagoras theorem,
$$\begin{gathered} {\mathrm{OQ}}^2+{\mathrm{OP}}^2={\mathrm{PQ}}^2 \\ \Rightarrow {24}^2+{10}^2={\mathrm{PQ}}^2 \\ \Rightarrow {\mathrm{PQ}}^2=576+100 \\ \Rightarrow {\mathrm{PQ}}^2=676 \\ \Rightarrow \mathrm{PQ}=26\mathrm{cm} \end{gathered}$$