Final answer:
Set the given side expressions of the equilateral triangle equal to each other to find the value of 'x', and then calculate the length of a side. All sides of the equilateral triangle measure 29 inches.
Step-by-step explanation:
To find the measurements of the sides of an equilateral triangle where the sides are given as expressions involving 'x', we need to set the three expressions equal to each other since all sides have the same length in an equilateral triangle. The expressions given are:
- x + 12 inches
- 2x - 5 inches
- 3x - 22 inches
Since all sides are equal, we equate the first expression to the second, and the second to the third:
- x + 12 = 2x - 5 (Equate the first and second)
- 2x - 5 = 3x - 22 (Equate the second and third)
By solving these equations simultaneously, we find the value of 'x' which will give us the side lengths of the triangle:
- x + 12 = 2x - 5
- x = 17
- 2x - 5 = 3x - 22
- 2(17) - 5 = 34 - 5
- 29 inches is the length of each side of the triangle.