My assignment says The perimeter of a rectangle is 30 cm.

Find the whole-number dimensions of the rectangle with:

a) the greatest area

b) the least area

can someone explain?

Let side be "a" cm. So another side is (30-2a) / 2=15-a

S=ab=a (15-a) = 15a-a^2 - parabola

maximum when a = - 15/-2=7.5 cm

When a=7.5 all sides are 7.5 cm

So it's a square. S=a*a=7.5*7.5=56.25 cm^2 - max

There is no global minimun for S. (look at the graphic)