The length and the width of the rug having an area of 40 square feet will be 5 feet and 8 feet respectively.
Area is defined as the space covered by any object in the two dimensional plane. Here it is given that the area of the rug should be 40 square feet and the length of the rug is 3 less then its width.
So to find out the length and the width we will form an equation.
Let the width is = x feet
So the length will be = x-3 feet
Now the area will be
[tex]x(x-3)=40[/tex]
[tex]x^2-3x-40=0[/tex]
By solving the quadratic equation
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(-3)\pm\sqrt{9+(4\times1\times40}}{2}[/tex]
[tex]x=\dfrac{3\pm13}{2}[/tex]
[tex]x=8 \ and \ \ x=-5.5[/tex]
Here the value of x will be positive because length cant be negative.
So the width of the rug will be x=8 feet
Length of the rug will be x-3= 8-3=5 feet
Hence the length and the width of the rug having an area of 40 square feet will be 5 feet and 8 feet respectively.
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