Let #l# be the length (longer side) of the rectangular garden, and #w# be the width(shorter side).
Perimeter = #2(l+w) = 60m#-----(1) given.
Area = #lxxw= 225m^2#------(2) given
(1) #=> 2l + 2w = 60#
#=> 2l = 60 - 2w#
#=> l = (60-2w)/2#
Substitute #l# in (2):
#=> w xx (60-2w)/2 = 225#
#=> 60w - 2w^2 = 225 xx 2 #
#=> -2w^2 +60 w -550=0#
#=> 2w^2 - 60 w +550 =0#
#=> w^2 - 30w + 225 =0#
Solving this quadratic equation:
# =>w^2 - 15w -15w +225=0#
#=> w(w-15) -15(w-15) = 0 #
#=> (w-15)(w-15) = 0 #
#=> w -15=0 #
#=> color(red)(w=15m)#
So, the width is #w=15m#.
#therefore# (1) #=> 2(l+w) =60#
#=> 2(l +15)= 60#
#=> 2l +30 =60#
#=> l = 30/2= 15#
# color(red)(l= 15m)#
That means the length of the rectangular garden is also #15m#
This implies that the garden is #color(red)(square)# shaped with #l= 15m # and #w=15m # i.e. each Side = #15m#
