Question

A rectangular garden has a perimeter of 48 cm and an area of 140 sq. cm. what is the width of this garden?

Answer 1

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:

`a+b=48` (1)
The area of the garden is the product between the two sides, and it is equal to
`140 cm^2`:

`a b = 140`

From (1), we find

`b=48 -a`
And by substituting this into (2)

`a(48-a)=140`

`a^2-48a+140 =0`
which gives two solutions:

`a=44.9`, to which corresponds
`b=48-a=48-44.9=3.1`

`a=3.1`, to which corresponds
`b=48-a=48-3.1=44.9`

So, the width of the garden is
`44.9 cm` while the length of the other side is
`3.1 cm`.