Final answer:
The dimensions of the open box with a square base constructed from 189 square inches of material and a height of 3 inches are Length = 9 inches, Width = 9 inches, Height = 3 inches. This is found by setting up a quadratic equation from the surface area formula and solving for the side length of the base.
Step-by-step explanation:
To find the dimensions of the box with a square base and a height of 3 inches, constructed from 189 square inches of material, we need to consider the surface area of the box.
Let the side length of the square base be s inches. The surface area of an open box (without the top) is calculated by surface area = base area + 4 * side area, which is s² + 4s(3).
We are given that the surface area is 189 square inches, so we can write the equation:
s² + 4s(3) = 189
s² + 12s - 189 = 0
This is a quadratic equation, which we can solve for s. Factoring the quadratic, we get:
(s + 21)(s - 9) = 0
The solution s = -21 is not possible for the dimensions of a box, so the side length s must be 9 inches. Therefore, the dimensions of the box are Length = 9 inches, Width = 9 inches, Height = 3 inches.
Option c) Length = 9 inches, Width = 9 inches, Height = 3 inches is the correct answer.