Arectangle 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