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 3/7 of the perimeter of a rectangle that has a side equal to x and a side that is 6 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 sides of rectangle

One side of the rectangle is $x$ and the other side is $x + 6$.

Step3: Find perimeter of rectangle

The perimeter of a rectangle is $2(l + w)$, so the perimeter of this rectangle is $2(x+(x + 6))=2(2x + 6)$.

Step4: Set up the equation

The perimeter of the square is $\frac{3}{7}$ of the perimeter of the rectangle. So the equation is $4x=\frac{3}{7}\times2(2x + 6)$.

Answer:

$4x=\frac{3}{7}\times2(2x + 6)$