What is the maximum possible area of a triangle inscribed in a semicircle of radius R cm__________?
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Answer: B. R2 cm2
Explanation
The maximum area triangle inside a semicircle uses the semicircle diameter as its base. The height of this inscribed triangle equals the radius of the supporting semicircle. Multiplying one half by the base length and the radius gives the resulting area formula. A semicircle is bounded by its diameter and curved arc, constraining any inscribed geometric figures. The height from the diameter to the highest point on the circular arc equals the radius. Triangles maximize their area when their altitude is perpendicular to and maximized across the base.
Maximizing geometric areas within fixed boundaries is a fundamental concept in architectural design. Calculus and optimization problems often involve finding extreme values for inscribed geometric shapes. Engineering components frequently require maximizing internal dimensions while adhering to strict spatial constraints. Option a represents a linear dimension rather than a squared area measurement. Option c underestimates the maximum possible area by missing a necessary factor of two. Option d overestimates the maximum area by applying an incorrect height or base scaling factor.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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