Premier bank is planning to have a new building constructed

When you start writing equations, you find the problem statement has a number of holes. We'll do it this way.

Let L, W, N represent the length in feet, width in feet, and number of floors (count). Then it seems we can write
.. L = W +40 . . . . . length is 40 ft more than width
.. 10LW +35000N = 1180000 . . . . . cost is based on foundation area and number of floors. (Here, we assume the 1st floor is sandwiched between the foundation at ground level and whatever it is that is 12 ft high and costs 35,000.)
.. 2(L +W) = 3*(12N) . . . . the height is 12 ft times the number of floors, and the perimeter is 3 times that.

These give rise to a quadratic equation.
.. 10L(L -40) +35000(L +(L -40))/18 = 1180000
Eliminating fractions and dividing by 10, we get
.. 9L^2 +3140L -1132000 = 0
The positive solution is
.. L = (10/9)*(-157 +√126529) ≈ 220.788

There is one solution and it is viable.


The building is approximately 220.8 ft by 180.8 ft and 22.3 floors high.