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Luda [366]
3 years ago
7

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.

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
7 0
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

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