For this equation we need to write two equations to solve for our 2 variables, length and width.
First equation where length is three less than three times the width
[tex]l = 3w - 3[/tex]
Second equation is the equation for perimeter- all sides added up
[tex]perimeter = 2l + 2w [/tex]
Let's use substitution where we substitute length for 3w-3. We can do this because they are equal and then we can solve the 1 variable equation.
We know that perimeter is 34 meters.
[tex]34 = 2(3w - 3) + 2w[/tex]
Distribute the 2 to 3w-3
[tex]34 = 6w - 6 + 2w[/tex]
Simplify by combining like terms
[tex]34 = 8w - 6[/tex]
Add 6 to both sides
[tex]8w = 40[/tex]
Divide both sides by 8 to isolate the x
[tex]w = 5[/tex]
The width is 5 meters.
Substitute it into length=3w-3 to find out what length is
[tex]l = 3(5) - 3[/tex]
Simplify
The length is 12 meters.
The dimensions of the rectangle is that the length is 12 meters and the width is 5 meters.
