Step 1: Understanding the Concept:
This is a problem in ergonomics and universal design. The goal is to determine a placement for a critical control (an emergency latch) that satisfies two constraints: it must be accessible to all intended users (adults) and inaccessible to unintended users (children).
Step 2: Analyzing the Constraints:
Child Safety: The latch must be high enough so that children cannot reach it. The problem states that the tallest child is shorter than the shortest adult. This means any height that is accessible to the shortest adult will automatically be inaccessible to any child. Therefore, we only need to focus on adult accessibility.
Adult Accessibility (in an emergency): For an emergency exit to be effective, every adult must be able to operate it. This includes the shortest adult in the household.
Step 3: Evaluating the Options:
(A) The height of the tallest adult in the family: If the latch is placed at a height convenient for the tallest adult, it may be too high for the shortest adult to reach, especially in a panic situation. This violates the accessibility requirement.
(B) The height of the shortest adult in the family: If the latch is placed at a height that is reachable by the shortest adult, then all taller adults will also be able to reach it. This ensures that every adult in the household can use the emergency exit. This is the principle of "designing for the extremes."
(C) The average height of the child in the family: This is irrelevant and unsafe. It's used to determine what children *can* reach, not what they *can't*.
(D) The average height of the tallest adult male and tallest adult female: An average height might still be too high for the shortest adult in the family (e.g., an elderly person or a person of short stature).
Step 4: Final Answer:
To ensure universal accessibility for all adults while keeping it out of reach of children (as per the given assumption), the latch height should be determined based on the reach of the shortest adult.