Verified answer

Let the width be w and the length be l.

=> 2w + l = 43

and lw = 221

=> w(43 - 2w) = 221

=> 2w² - 43w + 221 = 0

i.e. (2w - 17)(w - 13) = 0

so, w = 17/2 or 13

=> width 8.5 feet and length 26 feet

or width 13 feet and length 17 feet.

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Perimeter = 2x +y = 43

Area = 2xy = 221

y = 43 - 2 x

2x (43 -2x ) = 221

86 x -4 x^2 - 221 = 0

4 x^2 - 86 x + 221 =- 0

x^2 - 21.5 x + 55.25 = 0

X= + 21.5/2 +/- 1/2 (21.5^2 - 4x55.25)^1/2

X = 18.5 y = 6

Check: 2x + y = 2 x 18.5 + 6 = 43

2xy = 2x 18.5 x 6 = 222

L * W = 221 : eqn1

L + 2 W = 43: eqn2

L = 43 - 2 W from eqn 2

(43-2W)(W) = 221 sub in eqn 1

43 W - 2 W^2 = 221

2 W^2 - 43 W + 221 = 0

(2 W -17 )(W-13 ) = 0

W = 17/2: L = 43-(17/2)2 = 26

W = 13 ; L = 43-2(13) = 43-26 = 17

ok he have 3 sides and their length is 43 feets let Length = x and width = y

and that he has 2x + y = 43

Since Area is 221 So xy = 221

x = 221/y By Substituting in the first one

2(221/y) + y = 43 Multiply y

442 + y^2 = 43y

y^2 - 43y + 442 = 0

(y-26)(y-17) = 0

So y = 26 or 17 So the Width = 26Feets or 17 Feets

When Width = 26 , Length = 8.5

When Width = 17 , Length = 13