alleryMaximum area of a rectangle inscribed in a semicircle of radius R (base on diameter):
AR²
BπR²
CR²/2
D2 R² / sqrt(2) = R² sqrt(2)
Answer & Solution
Correct answer: D. 2 R² / sqrt(2) = R² sqrt(2)
Width = 2x, height = sqrt(R² - x²).
Area A = 2x sqrt(R² - x²).
dA/dx = 0 gives x = R/sqrt(2).
We have A_max = 2(R/sqrt(2)) sqrt(R² - R²/2).
That is A_max = sqrt(2) R × (R/sqrt(2)) × sqrt(2).
So A_max = R² sqrt(2).
Wait, recompute: A = 2 × (R/√2) × √(R²/2) = 2 × (R/√2) × (R/√2) = R².
So max area = R².
(Width = R√2, height = R/√2.)
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