The perimeter of a rectangular flower garden is 60m and its area is 225 m^2. How do you find the length of the garden?

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Answer 1 · 2018-03-07T10:27:45

Length of the garden = 15m

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#