9514 1404 393
Answer:
205 ft
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is (6w-17) and the area is ...
A = LW
7585 = (6w-17)(w)
6w² -17w -7585 = 0
Perhaps most straightforward is using the quadratic formula to solve this.
For ax² +bx +c = 0, the solution is x = (-b±√(b²-4ac))/(2a). For the above quadratic, the solution is ...
[tex]x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot6\cdot(-7585)}}{2\cdot6}=\dfrac{17\pm\sqrt{182329}}{12}\\\\x=\dfrac{17\pm427}{12}=\{-34\frac{1}{6},37\}[/tex]
The width is 37 feet, so the length is ...
6(37) -17 = 205 . . . feet
The length of the rectangle is 205 feet.
