Verified Answer :

apologiabiology

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

Cricetus

The maximum area will be "400 cm²"

Given:

Perimeter = 80 cm

then,

  • \(2(l+x) = 80 \ cm\)

Length,

  • \(l = (40-x)cm\)

Area,

  • = \(lx\)

        = \((40-x)x \ cm^2\)

For, Area to be maximum

→                  \(\frac{dA}{dx} =0\)

→ \(\frac{d}{dx} (40-x)(x)=0\)

→           \(40-2x =0\)

→                   \(2x =40\)

→                     \(x = \frac{40}{2}\)

→                        \(= 20\)

hence,

The maximum area,

= \((40-20)20\)

= \(20\times 20\)

= \(400 \ cm^2\)

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