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