Final answer:
To find the dimensions of the rectangular cake with a given volume, one would set up an equation based on the volume formula for a rectangular prism, and solve for width to determine length and height.
Step-by-step explanation:
The question asks to find the dimensions of a rectangular cake that must have a certain volume, with relationships provided between the length, width, and height. We are told the cake needs a volume of 192 cubic inches, the length should be twice as long as the width, and the height should be 2 inches greater than the width. To solve this, we can set up an equation using the volume formula for a rectangular prism, which is volume = length x width x height (V = lwh). We'll use w for the width, 2w for the length (as it's twice the width), and w + 2 for the height (since it's 2 inches more than the width). Our equation becomes:
192 = w x (2w) x (w + 2)
After setting up the equation, we simplify and solve for w:
192 = 2w2(w + 2)
We would then distribute and form a cubic equation, solve for w, and calculate the other dimensions from that.