Final answer:
The problem is solved by setting up an algebraic equation based on the given volume and the relationships between the container's dimensions, then solving for the width to eventually find all dimensions.
Step-by-step explanation:
The problem given is a classic example of an algebraic geometry problem where we have to find the dimensions of a rectangular container given its volume and the relationships between its length, width, and height.
Let the width of the container be w cm. According to the problem, the length is w + 3 cm, and the height is 3 times as tall as the length, so the height is 3(w + 3) cm. Given that the volume of the container is 400 cubic centimeters, we can write the equation for volume as:
V = l × w × h
Plug the values into the equation:
400 = (w + 3) × w × 3(w + 3)
Solving this equation will give us the value of w, from which we can find the length by adding 3 to w and the height by multiplying the length by 3.