An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m2 find the dimensions of the garden

For this case, the first thing we must do is define variables.

We have then:

x: length of the garden

y: width of the garden

The garden area is:

The perimeter of the garden is:

Rewriting the perimeter:

Substituting in the area we have:

Completing squares:

We discard the negative root:

Then, the other dimension is:

The dimensions of the garden are:

so, converting firstly the mixed fractions to improper fractions and then "adding".