Write a simplified rational expression for the ratio of the garden’s perimeter to its area.

Question

Farmer fred want to fence in his square garden with side of length 3x. Write a simplified rational expression for the ratio of the garden’s perimeter to its area.

Answer 1

The perimeter of a square with side of length s is 4s.  In this case the length of each side is 3x, so the perimeter is 4 * 3x = 12x.

 

The area of a square is s².  In this case, that means (3x)² = 9x².

 

So the ratio of the perimeter to the area is 12x / 9x².  Simplifying this gets 4/3x.

Answer 2

Since the garden is square, each side has the same length = 3x.

 

Area = side² = (3x)² = 9x²

 

Perimeter = 4*side = 4*3x = 12x

 

Perimeter/Area = 12x/9x² = (4*3*x)/(3*3*x*x) = 4/3x