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

question 32

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

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Definitions:

Liberalism

An approach towards politics and ethics that advocates for individual liberty, the agreement of the governed, and uniformity in legal standards.

European Enlightenment

An intellectual movement in 17th and 18th centuries emphasizing reason and individualism rather than tradition; heavily influencing the development of Western philosophy, political thought, and society.

Deism

Enlightenment thought applied to religion; emphasized reason, morality, and natural law.

Junípero Serra

An 18th-century Franciscan friar known for founding several missions in what is now California, contributing to the Spanish colonization of the region.