A rectangular back yard ice rink is to have an area of 1200m*2, and will be surrounded by boards.

a) What are the dimensions of the ice rink that can be enclosed with the least cost of boards?

b) if one board is 2.0 m long, how many boards would you need to enclose the rink.

a) The dimensions of the rectangle are width = 34.64 and length = 34.64.

b) If one board is 2m long there needs to be 70 boards to enclose the whole ring.

Step-by-step explanation:

The area of a rectangle is given by:

area = width*height

In order to compute the amount of boards that will be needed to enclose the rink with the least cost we need to find the rectangle with area equal 1200 m² that has the smallest possible perimeter. This happens when the width and the height of the rectangle are equal, so we have:

area = width*width

1200 = width²

width² = 1200

width = sqrt (1200) = 34.64m

So the height and the with of the rink must be 34.64 m.

The perimeter of the rink is:

perimeter = 2*width + 2*height = 2*34.64 + 2*34.64 = 138.56 m

Since each board is 2m the amount of boards needed is given by the division of the perimeter by the length of the board. We have:

number of boards = 138.56/2 = 69.28

Since there won't be a 0.28 board, then the number must be rounded up to 70.