# A wire 60 cm long is to be cut into two pieces. One of the pieces will be bent into the shape of a square and the other into the shape of an equilateral triangle, as shown in the diagram below:

a diagram showing a 60 cm wire cut into two pieces of length x and 60 minus x respectively. The wire of length x is bent into a square with side length x over 4 cm. The wire of length 60 minus x is bent into an equilateral triangle with sides of length 60 minus x over 3 cm

The wire is to be cut in order that the sum of the areas of the square and the triangle is to be a maximum. An equation that can be used to model the sum of the areas is A at x equals the sum of x squared over 16 and root 3 times quantity 60 minus x squared, over 18. Determine the boundaries and the corresponding areas. You need not solve further.

4. A cylindrical tank is to have a capacity of 1000 m³. It is to fit into a foundry that is 12 m wide with a height of 11 m.