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 4 more than x. show your work here

Explanation:

Step1: Find perimeter of the square

The perimeter of a square with side - length $x$ is given by $P_{square}=4x$ (since perimeter of a square $P = 4s$ and $s = x$).

Step2: Find perimeter of the rectangle

The sides of the rectangle are $x$ and $x + 4$. The perimeter of a rectangle $P=2(l + w)$, so $P_{rectangle}=2(x+(x + 4))=2(2x + 4)$.

Step3: Set up the equation

The perimeter of the square is the same as $\frac{1}{3}$ of the perimeter of the rectangle. So the equation is $4x=\frac{1}{3}\times2(2x + 4)$.

Answer:

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