Question

If the diagonals of the rhombus PQRS, PR and
SQ are 30 cm and 16 cm respectively, find the
length of its sides.
​

Answer 1

Let 'O' be the point of intersection of the diagonals PR & SQ.

In a rhombus (& square, rectangle, parallelogram) diagonals divide each other equally i.e. bisect each other at 90°

So, PO = OR = (PR/2) = 15.

Similarly SO = OQ = 8.

Now, in ∆POQ,

$PQ = \sqrt{ {PO} ^{2} + {OQ}^{2} }\\</p><p>So,\:\:PQ = \sqrt{ {15} ^{2} + {8}^{2} } = \sqrt{289} = 17cm.</p><p>$

In rhombus, all sides are equal..

So, PQ = QR = RS = SP = 17cm.