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Sagot :
The area of a rectangle is given by the following expression:
[tex]\text{area}=\text{length}\cdot\text{width}[/tex]We know that the length of the parking lot is 9 yards greater than the width, this means that if we add 9 yards to the width we will have the length.
[tex]\text{length}=\text{width}+9[/tex]By applying the second expression on the first one and making it equal to the area of the parking lot we can determine the width.
[tex]\begin{gathered} 360=(\text{width}+9)\cdot\text{width} \\ 360=width^2+9\cdot width \\ \text{width }^2+9\text{width}-360=0 \end{gathered}[/tex]We need to solve the second degree equation to determine the width.
[tex]\begin{gathered} \text{width}=\frac{-9\pm\sqrt[]{9^2-4\cdot1\cdot(-360)}}{2\cdot1} \\ \text{width}=\frac{-9\pm\sqrt[]{81+1440}}{2}=\frac{-9\pm39}{2} \\ \text{width}=\frac{-9+39}{2}=\frac{30}{2}=15 \end{gathered}[/tex]The width of the parking lot is 15 yards.
The length is the width added by 9 yards, which is equal to 24 yards.
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