The maximum area of a triangle inscribed in a | vedclass

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Question

(D) For a triangle inscribed in a semicircle,the base of the triangle is the diameter of the semicircle,and the height is the radius of the semicircle

Vedclass · Accepted Answer

$225$

Vedclass · Answer

(D) For a triangle inscribed in a semicircle,the base of the triangle is the diameter of the semicircle,and the height is the radius of the semicircle.Given,diameter $d = 30 \, cm$.Therefore,radius $r = \frac{d}{2} = \frac{30}{2} = 15 \, cm$.The base of the triangle $b = 30 \, cm$.The maximum height of the triangle is equal to the radius of the semicircle,$h = 15 \, cm$.Area of the triangle $= \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Area $= \frac{1}{2} 	imes 30 	imes 15 = 15 	imes 15 = 225 \, cm^{2}$.

The maximum area of a triangle inscribed in a semicircle with diameter $30 \, cm$ is $\ldots \ldots \ldots \, cm^{2}$.

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