A square with sides x + 2 and an equilateral triangle of sides with 2x have equal perimeters x = what?

4(x+2) = 3(2x)

Solve for x.

To find the value of x, we can set up an equation based on the given information.

Let's start by finding the perimeter of the square. The perimeter of a square is given by the formula P = 4s, where s is the length of its sides. In this case, the sides of the square are x + 2. Therefore, the perimeter of the square is 4(x + 2).

Next, let's find the perimeter of the equilateral triangle. The perimeter of an equilateral triangle is given by the formula P = 3s, where s is the length of its sides. In this case, the sides of the equilateral triangle are 2x. Therefore, the perimeter of the equilateral triangle is 3(2x), which simplifies to 6x.

Since the given information states that the square and the equilateral triangle have equal perimeters, we can set up an equation:

4(x + 2) = 6x

Now, let's solve for x:

4x + 8 = 6x (distributing 4 to x and 2)
8 = 6x - 4x (subtracting 4x from both sides)
8 = 2x (combining like terms)

To isolate x, divide both sides of the equation by 2:

8/2 = 2x/2
4 = x

Therefore, x = 4.