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 4/5 of the perimeter of a rectangle that has a side equal to x and a side that is 7 more than x. show your work here

Explanation:

Step1: Find the perimeter of the square

The perimeter of a square with side length \(x\) is \(P_{square}=4x\).

Step2: Find the dimensions and perimeter of the rectangle

One side of the rectangle is \(x\), and the other side is \(x + 7\). The perimeter of a rectangle is \(P_{rectangle}=2(l + w)=2(x+(x + 7))=2(2x+7)=4x + 14\).

Step3: Set up the equation based on the given relationship

We know that \(P_{square}=\frac{4}{5}P_{rectangle}\). Substitute the expressions for the perimeters: \(4x=\frac{4}{5}(4x + 14)\).

Answer:

\(4x=\frac{4}{5}(4x + 14)\)