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 an equilateral triangle with side length x is the same as the perimeter of a rectangle that has a side equal to the side of the triangle, as well as a side that is 5 units shorter than the side of the triangle.
show your work here

Explanation:

Step1: Find perimeter of equilateral triangle

The perimeter of an equilateral triangle with side - length $x$ is $3x$ since an equilateral triangle has 3 equal sides.

Step2: Find dimensions of rectangle

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

Step3: Find perimeter of rectangle

The perimeter of a rectangle is given by $2(l + w)$. Here, $l=x$ and $w=x - 5$, so the perimeter is $2(x+(x - 5))$.

Step4: Set perimeters equal

Since the perimeters are the same, we set up the equation.

Answer:

$3x=2(x+(x - 5))$