Whether it is cost, time or distance, we are often trying to minimise things. Usually we have restrictions which are key to determining the minimum possible value.
With a partner, come up with at least two scenarios where you would have a fixed area, but are flexible with the dimensions (perimeter). It does not need to be a rectangle.
Consider the possible scenario below which requires minimising the perimeter for a particular area.
A rectangular wedding cake needs to feed $80$80 people. One standard serving of cake should have a top area of about $20$20 cm2. It has an expensive decoration around the edge of the cake which costs $\$4.35$$4.35/cm. We want to find the dimensions of the cake that will minimise the cost of the decoration. Work through the questions below to find the best dimensions for the cake.
We typically see circular or rectangular cakes, but not triangular or hexagonal, why do you think that is? Consider both practical and mathematical reasons.
Determine the minimum perimeter of a rectangle with a given area by constructing a variety of rectangles, using a variety of tools and by examining various values of the side lengths and the perimeter as the area stays constant