Question

PQRS is a rhombus. The diagonals PR and QS bisect each other at a point O such that
PR=24cm and QS=10cm. Find the perimeter of the rhombus.

Answer 1

Answer:

52 units

Step-by-step explanation:

PQRS is rhombus [given]

diagonals of a rhombus bisect each other at an angle of 90 degrees

diagonals of a rhombus bisects each other

thus,

PO=OR=0.5*PR

thus,PO=OR=0.5*24=12 UNITS

AND,

OQ=OS=0.5*QS

QO=OS=0.5*10=5 UNITS

in triangle ROQ,

angle ROQ=90 degrees [diagonals bisect each others at 90 degrees]

thus in triangle ROQ by pythagoras theorm

RQ^2=OR^2+ OQ^2

RQ^2=12^2+5^2

RQ^2=144+25

=169

RQ^2=169 THUS,

RQ=13

PQ=QR=RS=PS   [ALL SIDES OF A RHOMBUS ARE EQUAL]

THUS,

PQ=QR=RS=PS=13 UNITS

PERIMETER [PQRS]=PQ+QR+RS+PS

=13+13+13+13

=52 UNITS

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