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27=lw; 24=2l+2w; l+w=24/2; l+w=12; l=12-w; 27=(12-w)w; 27=12w-w^2; w^2-12w+27=0; (w-9)(w-3)=0; w=9, w=3; l=12-9; l=3.....ans; w=9...ans
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A=  27 ft^{2} (Product of the roots/ dimensions)
P= 24 ft. (Sum of the dimensions)
Standard form: a x^{2} +  (-\frac{b}{a}) + \frac{c}{a} =0, wherein - \frac{b}{a} is the sum, and  \frac{c}{a} is the product.
P= \frac{2L+2W}{2} = \frac{24}{2}
P=12 (-1) 
Substitute the value and it will become:
 x^{2} -12x+27=0, (Let's solve by factoring)
(x-3)(x-9)=0, Simplify then.
x=3, x=9
Therefore the length is 9 ft. and the width is 3 ft.
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