Question

Does dose anyone know how to solve this?

Answer 1

Width of rectangle = 6 m

Length of rectangle = 11 m

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:
`Area=Length * Width`

Putting values and finding w

`Area=Length * Width\\66=(3w-7)(w)\\66=3w^2-7w\\3w^2-7w-66=0\\`

Solve using quadratic formula:
`w=(-b\pm√(b^2-4ac))/(2a)`

We have a=3, b=-7, c=-66

Putting values and finding w

`w=(-b\pm√(b^2-4ac))/(2a)\\w=(-(-7)\pm√((7)^2-4(3)(-66)))/(2(3))\\w=(7\pm√(49+792))/(6)\\w=(7\pm√(841))/(6)\\w=(7\pm29)/(6)\\w=(7+29)/(6)\:,\:w=(7-29)/(6)\\w=6, w=-3.6`

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