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The area of the garden is 160 meter squared.Suppose the length of the garden is 3m more than twice its width.What is the length of the garden?

Sagot :

[tex]w-width\\\\2w+3-length\\\\160m^2-area\ of\ the\ garden\\\\w\time(2w+3)-area\ of\ the\ garden\\\\w(2w+3)=160\\\\2w^2+3w-160=0[/tex]

[tex]a=2;\ b=3;\ c=-160\\\\\Delta=b^2-4ac\to\Delta=3^2-4\cdot2\cdot(-160)=9+1240=1249\\\\w_1=\frac{-b-\sqrt\Delta}{2a};\ w_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{1249}\approx35.34\\\\w_1=\frac{-3-35.34}{2\cdot2} < 0;\ w_2=\frac{-3+35.34}{2\cdot2}=\frac{32.34}{4}=8.085\ (m)\\\\length\approx2\cdot8.085+3=19.17\ (m)[/tex]
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