Find the dimensions of the petting area.

Question

The director of the Glen Island Zoo wants to use 170 m of fencing to enclose a rectangular petting area of 1750 m^2.

Answer 1

We're given 2 bits of information about this petting zoo...the amount of fencing used to enclose it and the area

 

Let's call the length of the rectangle l and the width w.

 

The fencing goes around the outside of the rectangle, which is known as the perimeter.  Therefore  170m (the amount of fencing) is equal to the perimeter.  The perimeter is 2 x l + 2 x w.  So...

 

2l + 2w = 170m   Divide by 2   and l + w = 85 m

 

The formula for area of a rectangle is l x w.  So...

 

lw = 1750 m² 

 

We can adapt the perimeter equation to get everything in terms of 1 variable:  l = 85 - w

Plug that into the area equation: w (85 - w) = 1750  =>  85w - w² = 1750 => w² - 85w + 1750 = 0

Factor this:  (w - 35) (w - 50) = 0

 

The solutions are 35 and 50.  The dimensions are 35 m x 50 m