Question

The length of a rectangles is 3 meters less than 3 time the width. The perimeter is 34 meters.

Answer 1

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
$l = 3w - 3$
Second equation is the equation for perimeter- all sides added up
$perimeter = 2l + 2w$
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.
$34 = 2(3w - 3) + 2w$
Distribute the 2 to 3w-3
$34 = 6w - 6 + 2w$
Simplify by combining like terms
$34 = 8w - 6$
Add 6 to both sides
$8w = 40$
Divide both sides by 8 to isolate the x
$w = 5$
The width is 5 meters.
Substitute it into length=3w-3 to find out what length is
$l = 3(5) - 3$
Simplify
The length is 12 meters.

The dimensions of the rectangle is that the length is 12 meters and the width is 5 meters.