Statement I: Among all rectangles of a given perimeter

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Statement I: Among all rectangles of a given perimeter, the square has the largest area. Also, among all rectangles of a given area, the square has the least perimeter. Statement II: For x>0x>0 and y>0y>0, if x+y=constantx+y=\text{constant}, then xyxy is maximum when y=xy=x; and if xy=constantxy=\text{constant}, then x+yx+y is minimum when y=xy=x.

Related theory

Browse the problem library