Question

write a linear equation to model the scenario. use x for the unknown variable. do not simplify the equation or solve.
the perimeter of a square with side length x is the same as ⅓ of the perimeter of a rectangle that has a side equal to x and a side that is 1 more than x.
show your work here

Explanation:

Step1: Find perimeter of square

The perimeter of a square with side - length $x$ is $4x$ (since perimeter of square = 4×side - length).

Step2: Find perimeter of rectangle

The sides of the rectangle are $x$ and $x + 1$. The perimeter of a rectangle is $2(l+w)$, so the perimeter of this rectangle is $2(x+(x + 1))=2(2x + 1)$.

Step3: Set up the equation

We are given that the perimeter of the square is the same as $\frac{1}{3}$ of the perimeter of the rectangle. So, $4x=\frac{1}{3}\times2(2x + 1)$.

Answer:

$4x=\frac{1}{3}\times2(2x + 1)$