We can call a the width of the garden and b the length of the other side.
The perimeter of the garden is the sum of the two sides, and it is equal to 48 cm:
[tex]a+b=48[/tex] (1)
The area of the garden is the product between the two sides, and it is equal to [tex]140 cm^2[/tex]:
[tex]a b = 140[/tex]
From (1), we find
[tex]b=48 -a[/tex]
And by substituting this into (2)
[tex]a(48-a)=140[/tex]
[tex]a^2-48a+140 =0[/tex]
which gives two solutions:
[tex]a=44.9[/tex], to which corresponds [tex]b=48-a=48-44.9=3.1[/tex]
[tex]a=3.1[/tex], to which corresponds [tex]b=48-a=48-3.1=44.9[/tex]
So, the width of the garden is [tex]44.9 cm[/tex] while the length of the other side is [tex]3.1 cm[/tex].
