Question

If the length of each side of the Rhombus PQRS is 15cm . if diagonal PR is 24 cm find the length of the other diagonal QS

Answer 1

in the diagram,
as the diagnols of a rhombus bisect each other,
OP = OR ---------------------------1
PR=24cm (given)-----------------2
similarly  QO = OS--------------------------3

now 2*OP =24(with 1 and 2)
OP= 12 cm = OR
angle OPQ =90 degree (diagnols bisect)
in triangle POQ,
PO square+ OQ square = PQ square (pythagoras theorem)
(12)square + OQ square =  (15) square
OQ square = 225 - 144
OQ square = 81
OQ= 9
 
OQ = OS (from 3)
2OQ = SQ
2 * 9 =SQ (diagnol 2)
thus,
the other diagnol SQ = 18cm

hope it helps!!!!!