Question

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

Answer 1

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