The maximum area of a triangle inscribed in a | vedclass

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Question

(C) Let the radius of the semicircle be $r = 10 \, cm$.For a triangle inscribed in a semicircle,the base of the triangle is the diameter of the semici

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(C) Let the radius of the semicircle be $r = 10 \, cm$.For a triangle inscribed in a semicircle,the base of the triangle is the diameter of the semicircle,which is $d = 2r = 2 	imes 10 = 20 \, cm$.The height of the triangle is the perpendicular distance from the diameter to the circumference,which is maximum when the vertex lies at the midpoint of the arc,making the height equal to the radius $r = 10 \, cm$.The area of a triangle is given by the formula: $	ext{Area} = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Substituting the values: $	ext{Area} = \frac{1}{2} 	imes 20 	imes 10 = 100 \, cm^2$.Thus,the maximum area is $100 \, cm^2$.

The maximum area of a triangle inscribed in a semicircle having radius $10 \, cm$ is $\ldots \ldots \ldots \, cm^2$.

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