Respuesta :
ANSWER
Length: 23 ft
Width: 9 ft
EXPLANATION
The area of a rectangle is:
[tex]A=L\times W[/tex]Where L and W are length and width. We know that for this rectangle the area is 207 ft²
and the length is 5 more than twice its width:
[tex]L=5+2W[/tex]We have a system of equations:
[tex]\begin{cases}L=5+2W \\ LW=207\end{cases}[/tex]We can replace L from the first equation into the second equation:
[tex](5+2W)W=207[/tex]And solve for W. To do this we have to rewrite the equation above:
[tex]2W^2+5W-207=0[/tex]We have a quadratic equation, that can be solved with:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In this case x = W, a = 2, b = 5 and c = -207:
[tex]\begin{gathered} W=\frac{-5\pm\sqrt[]{5^2-4\cdot2\cdot(-207)}}{2\cdot2} \\ W=\frac{-5\pm\sqrt[]{25+1656}}{4} \\ W=\frac{-5\pm\sqrt[]{1681}}{4} \\ W=\frac{-5\pm41}{4} \end{gathered}[/tex]Note that we have here two results, one negative and one positive. The only valid result is the positive one, because the width can't be negative:
[tex]W=\frac{-5+41}{4}=\frac{36}{4}=9[/tex]The width of the rectangle is 9 feet.
Then, to find the length we just have to replace the width into the first equation:
[tex]L=5+2\cdot W=5+2\cdot9=5+18=23[/tex]The length is 23 feet.
