Find the Dimensions of the Rectangle Enclosed in the Semicircle $y=\sqrt{144-x^{2}}$

question 30

Multiple Choice

Find the dimensions of the rectangle enclosed in the semicircle $y=\sqrt{144-x^{2}}$ with the largest possible area.

• A) 5 in. \(x\) 7 in.
• B) \(6\) in. \(x\) \(6\) in.
• C) \(12 \sqrt{2}\) in. \(x\) \(6 \sqrt{2}\) in.
• D) \(6 \sqrt{2}\) in. \(x\) \(6 \sqrt{2}\) in.

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Definitions:

High-risk Areas

Regions that are highly susceptible to natural disasters, environmental hazards, or other significant risks.

Thrust Fault

A geological fault in which the upper block, or hanging wall, is pushed up and over the lower block, or footwall, often forming mountains or ridges.

Sea Level

The average height of the ocean's surface between the high and low tide, used as a reference point in measuring elevation and depths on Earth.

Marine Terraces

Flat, bench-like surfaces parallel to the shoreline that are formed by marine erosion and changes in sea level.