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 1/3 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 the perimeter of the square

The perimeter of a square is calculated by \(P = 4\times\) side length. Given the side length is \(x\), so the perimeter of the square is \(4x\).

Step2: Find the perimeter of the rectangle

The rectangle has sides \(x\) and \(x + 4\). The perimeter of a rectangle is \(P=2\times(\text{length}+\text{width})\), so the perimeter of the rectangle is \(2(x+(x + 4))=2(2x + 4)\).

Step3: Set up the equation

Since the perimeter of the square is the same as \(\frac{1}{3}\) of the perimeter of the rectangle, we get the equation \(4x=\frac{1}{3}\times2(2x + 4)\)

Answer:

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