Question

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

Answer 1

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:

`xy = 5000`

The perimeter of the garden is:

`2x + 2y = 300`

Rewriting the perimeter:

`x + y = 150`

`y = 150-x`

Substituting in the area we have:

`x (150-x) = 5000`

`150x-x ^ 2 = 5000`

Completing squares:

`x ^ 2-150x = -5000`

`x ^ 2-150x + (- 75) ^ 2 = -5000 + (- 75) ^ 2`

`(x-75) ^ 2 = 625`

We discard the negative root:

`(x-75) = √(625)`

`(x-75) = 25`

`x = 25 + 75`

`x = 100`

Then, the other dimension is:

`y = 150-x`

`y = 150-100`

`y = 50`

Answer:

The dimensions of the garden are:

`x = 100`

`y = 50`