Question

A piece of cardboard that is 14 inches by 18 inches is used to form a box with an open top by cutting away congruent squares with side lengths, x, from the corners. Write an equation y, in terms of x, in standard form to model the surface area of the open box after the corners are cut away.

Answer 1

We have to add all the areas formed:

Area of a rectangle: Length x width

A1 =(18-2x) (14-2x) = 252-36x -28x+4x^2 = 4x^2-64x +252

A2 = (14-2x) x = 14x-2x^2

A4 = (14-2x) x = 14x-2x^2

A5 = (18-2x)x = 18x-2x^2

A3 = (18-2x)x = 18x-2x^2

Surface area (y) = A1+A2+A3+A4+A5

SA = (4x^2-64x +252) + ( 14x-2x^2) + ( 14x-2x^2) + (18x-2x^2)+ (18x-2x^2)

SA = 4x^2-2x^2-2x^2-2x^2-2x^2 - 64x +14x+14x+18x+18x +252

y (x) = -4x^2 +252