The maximum area of a triangle inscribed in a | vedclass

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(B) The diameter of the semicircle is $d = 50 \, cm$,so the radius is $r = 25 \, cm$.For a triangle inscribed in a semicircle,the base of the triangle

Vedclass · Accepted Answer

$625$

Vedclass · Answer

(B) The diameter of the semicircle is $d = 50 \, cm$,so the radius is $r = 25 \, cm$.For a triangle inscribed in a semicircle,the base of the triangle is the diameter of the semicircle $(b = 50 \, cm)$.The height of the triangle is the radius of the semicircle $(h = r = 25 \, cm)$ because the maximum height is achieved when the vertex is at the midpoint of the arc.The area of the triangle is given by the formula $A = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Substituting the values: $A = \frac{1}{2} 	imes 50 	imes 25 = 25 	imes 25 = 625 \, cm^{2}$.

The maximum area of a triangle inscribed in a semicircle with diameter $50 \, cm$ is ........... $cm^{2}$.

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