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.
