The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square​ kilometers, find the dimensions of the rectangle.

Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
[tex]x(2x - 6) = 2 {x}^{2} - 6x[/tex]

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

[tex]2 {x}^{2} - 6x = 108[/tex]
Subtract 108

[tex]2 {x}^{2} - 6x - 108 = 0[/tex]
Divide by 2.

[tex] {x}^{2} - 3x - 54[/tex]
[tex](x - 9)(x + 6) = 0[/tex]
Rule AB = 0, gives A is 0 or B is 0.

[tex]x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6[/tex]

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
[tex]x = 9[/tex]
Width
[tex]2x - 6 = 2 \times 9- 6 = 18 - 6 = 12[/tex]

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!