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 1/7 of the perimeter of a rectangle that has a side equal to x and a side that is 5 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 the formula $P_{square}=4x$.

Step2: Find the sides of the rectangle

One side of the rectangle is $x$ and the other side is $x + 5$.

Step3: Find perimeter of the rectangle

The perimeter of a rectangle is $P_{rectangle}=2(l + w)=2(x+(x + 5))=2(2x + 5)$.

Step4: Set up the equation

Since the perimeter of the square is $\frac{1}{7}$ of the perimeter of the rectangle, we have $4x=\frac{1}{7}\times2(2x + 5)$.

Answer:

$4x=\frac{1}{7}\times2(2x + 5)$