A rectangle is inscribed in a semi-circle of radius `r`with one of its – InterviewSolution

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1.	A rectangle is inscribed in a semi-circle of radius `r`with one of its sides on diameter of semi-circle. Find the dimensionsof the rectangle so that its area is maximum. Find also the area.
Answer» `b=sqrt(r^2-(a/2)^2` `b=sqrt(4r^2-a^2)/2` Area of A=`ab=a(sqrt(4r^2-a^2)/2)` diff with respect to a `(dA)/(da)=sqrt(4r^2-a^2)/2` `=a/21/21/sqrt(4r^2-a^2)*-2a` `(dA)/(da)=sqrt(4r^2-a^2)/2-a^2/(2sqrt(4r^2-a^2))=0` `(4r^2-a^2-a^2)/(2sqrt(4r^2-a^2))=0` `4r^2=2a^2` `a=pmsqrt2r` `b=sqrt(4r^2-a^2)/2=sqrt2r/2=4/sqrt2` Area=`r^2.`

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A rectangle is inscribed in a semi-circle of radius `r`with one of its sides on diameter of semi-circle. Find the dimensionsof the rectangle so that its area is maximum. Find also the area.