Question

question 18 (4 points) the square and equilateral triangle below have the same perimeter. find the value of x. you must show all handwritten work to earn full credit. (hint: an equilateral triangle has 3 sides that are the same length) 2.5x - 3 2x - 2

Explanation:

Step1: Write perimeter formulas

The perimeter of a square with side - length \(s\) is \(P_{square}=4s\). Here, \(s = 2.5x−3\), so \(P_{square}=4(2.5x - 3)=10x-12\). The perimeter of an equilateral triangle with side - length \(t\) is \(P_{triangle}=3t\). Here, \(t = 2x - 2\), so \(P_{triangle}=3(2x - 2)=6x-6\).

Step2: Set perimeters equal

Since the perimeters are equal, we set up the equation \(10x-12 = 6x - 6\).

Step3: Solve the equation for \(x\)

Subtract \(6x\) from both sides: \(10x-6x-12=6x - 6-6x\), which simplifies to \(4x-12=-6\). Then add 12 to both sides: \(4x-12 + 12=-6 + 12\), giving \(4x = 6\). Divide both sides by 4: \(x=\frac{6}{4}=\frac{3}{2}=1.5\).

Answer:

\(x = 1.5\)