anonymous 5 years ago find the area of the largest rectancle that can be inscribed in a semi-circle or radius 'a'

Your x must be$a/\sqrt{2}$Area=2xy Circle $x ^{2}+y ^{2}+a ^{2}$$y =\sqrt{a ^{2}-x ^{2}}$$A(x)=2x \sqrt{a ^{2}-x ^{2}}$$A'(x)=(2a ^{2}-4x ^{2})/\sqrt{a ^{2-x ^{2}}}=0$$x =a/\sqrt{2}$