A rectangle has a perimeter of 80 cm. If its width is x, express its length and area in terms of x, and find the maximum area.

Perimiter=2L+2W

w=x

P=80

80=2L+2x

diviide by 2

40=L+x

40-L=x

40-x=L

the area is found by legnth times width

LW or Lx

for a maximum area, try to get the legnths of the sides the same

therefor

L=W=x for max area

40=x+x

40=2x

divide 2

20=x

max area = legnth times width=20^2=400

note: all squares are rectangles, but not all rectangles are squares

L=40-x

A = (40-x) (x)

max area=400 cm^2