Answer:
Width of rectangle = 6 m
Length of rectangle = 11 m
Step-by-step explanation:
Let width of rectangle = w
Length of rectangle = 3w-7
Area of rectangle = 66 m²
We need to find length and width of rectangle
The formula used is: [tex]Area=Length \times Width[/tex]
Putting values and finding w
[tex]Area=Length \times Width\\66=(3w-7)(w)\\66=3w^2-7w\\3w^2-7w-66=0\\[/tex]
Solve using quadratic formula: [tex]w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a=3, b=-7, c=-66
Putting values and finding w
[tex]w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-(-7)\pm\sqrt{(7)^2-4(3)(-66)}}{2(3)}\\w=\frac{7\pm\sqrt{49+792}}{6}\\w=\frac{7\pm\sqrt{841}}{6}\\w=\frac{7\pm29}{6}\\w=\frac{7+29}{6}\:,\:w=\frac{7-29}{6}\\w=6, w=-3.6[/tex]
We get values of w as w=6 and w=-3.6
As we know width cannot be negative, so considering w = 6
So, Width = 6
Length = 3w-7 = 3(6)-7 = 18-7 = 11
So, Width of rectangle = 6 m
Length of rectangle = 11 m
