**Guide :High School **

# 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.

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+2Ww=xP=8080=2L+2xdiviide by 240=L+x40-L=x40-x=Lthe area is found by legnth times widthLW or Lxfor a maximum area, try to get the legnths of the sides the samethereforL=W=x for max area40=x+x40=2xdivide 220=xmax area =legnth times width=20^2=400note: all squares are rectangles, but not all rectangles are squaresL=40-xA=(40-x)(x)max area=400 cm^2**...