Final answer:
The height of the trough is calculated by assuming a rectangular cross-section and solving a system of equations based on the given total width of three sides and the cross-sectional area. The height is determined to be 4 cm.
Step-by-step explanation:
To find the height of the trough, we need to use the formula for the volume of a three-dimensional object with parallel sides, which is the cross-sectional area times the height (V = Ah). Given that the cross-sectional area (A) is 112 cm² and the width of the three sides of the trough is 30 cm in total, we can infer that the trough has a rectangular cross-section. If we assume the trough has a width (W) and a height (H) with a total perimeter (P) of 30 cm for the three sides involved in the cross-section (2W + H = 30 cm), we can write the equation for the cross-sectional area (W * H = 112 cm²).
We need to solve the system of equations:
- 2W + H = 30
- W * H = 112
If we express W from the first equation as W = (30 - H)/2 and substitute it into the second equation, we get:
((30 - H)/2) * H = 112
After simplifying the equation and solving for H, we find that the height of the trough is 4 cm.