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:

$(x-75) = \sqrt{625}$

$(x-75) = 25$

$x = 25 + 75$

$x = 100$

Then, the other dimension is:

$y = 150-x$

$y = 150-100$

$y = 50$

Answer:

The dimensions of the garden are:

$x = 100$

$y = 50$