Question

give a re tangle of perimeter 28 cm what will be it's maximum and minimum area​

Answer 1

Answer:

Explanation:

Let x and y be the respective sides of the given rectangle. By the condition given, one has that:2(x+y)=28

so that x=14−y

The area of a rectangle is given by A(x,y)=xy=(14−y)y=A(y) To maximize A(y)w.r.t. y,one finds its derivative w.r.t. y and sets it to zero, solving for y;

A‘(y)=14–2y=2(7−y)

So, y=7(cm) is the critical point of A that is also a maximizer. Then x=14–7=7(cm). The rectangle is thus a square of side length 7cm. with area 49cm2.