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 given by the formula $P_{square}=4x$.

Step2: Find dimensions and perimeter of rectangle

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

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:

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