Solve the Problem $\frac { \text { width } } { \text { height } } = \frac { 16 } { 8 + 3 \pi }$

question 379

Multiple Choice

Solve the problem.
-A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only one-fourth as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light. Neglect the thickness of the frame.

• A) \(\frac { \text { width } } { \text { height } } = \frac { 16 } { 8 + 3 \pi }\)
• B) \(\frac { \text { width } } { \text { height } } = \frac { 4 } { 8 + 3 \pi }\)
• C) \(\frac { \text { width } } { \text { height } } = \frac { 16 } { 8 + \pi }\)
• D) \(\frac { \text { width } } { \text { height } } = \frac { 16 } { 4 + 3 \pi }\)

---

Definitions:

Information Overload

Information overload describes a state where an individual is exposed to more information than they can effectively process, leading to overwhelming feelings or decision paralysis.

Proxemics

The study of how humans use space and distance in communication, including personal territory and physical proximity in interactions.

Physical Space

The physical environment or the tangible, external surroundings where human activities occur.

Listening

The act of actively paying attention to sound, with the intent of understanding and often responding to it.