Premier bank is planning to have a new building constructed. they would like the length of the building to be 40 feet longer than its width. to fit their needs, each floor of the building will add 12 feet to the height of the building.

the cost of the foundation of the building will be $10 per square foot. the cost for each successive floor of the building will be $35,000. they plan to spend $1,180,000 on construction.

they would also like the perimeter of the building to be 3 times the height of the building.

create a system of equations to model the situation above, and use it to determine how many of the solutions are viable.

note: the bank wants the building to be as close to their specifications as possible, but the solution does not need to include whole numbers in order to be considered viable.