Beth is moving into a new house and purchased cardboard boxes for packing her things. Each cardboard box has a square base and a height that is 5 inches shorter than the side length of the base. If x represents the side length of the base, which of the following functions represents the surface area, S, of the cardboard box?S(x) = 2x2 + 10xS(x) = 6x2 + 20xS(x) = 2x2 - 10xS(x) = 6x2 - 20x
The top also has an area of x^2 since the base and top are both congruent squares. The total base area is x^2+x^2 = 2x^2
The height h is 5 inches shorter than the base, so h = (base length) - 5 h = x-5
Each lateral side is of area h*x = (x-5)*x = x^2-5x
There are 4 lateral sides Total lateral area = 4*(area of one lateral side) Total lateral area = 4*(x^2-5x) Total lateral area = 4*x^2-4*5x Total lateral area = 4*x^2-20x
Add the total lateral area (4x^2-20x) to the total base area (2x^2)
Doing so gets us S(x) = Total Surface Area S(x) = (Area of bases) + (area of lateral sides) S(x) = (2x^2) + (4x^2-20x) S(x) = (2x^2+4x^2) - 20x S(x) = 6x^2 - 20x which is why the answer is choice D