Question

A square has side lengths of 2x inches. An equilateral triangle has side lengths of (2x+13)

inches. If the square and the triangle have the same perimeter, what is the value of x?

Alternative Text

Select the correct answer.

Answer 1

To find the perimeter of the square, we multiply the length of one side by 4 since a square has four equal sides. Therefore, the perimeter of the square is 4 * 2x = 8x.

To find the perimeter of the equilateral triangle, we multiply the length of one side by 3 since an equilateral triangle has three equal sides. Therefore, the perimeter of the triangle is 3 * (2x + 13) = 6x + 39.

Since the square and the triangle have the same perimeter, we can set up the equation:

8x = 6x + 39

Subtracting 6x from both sides, we get:

2x = 39

Dividing both sides by 2, we find:

x = 19.5

Therefore, the value of x is 19.5.