Final answer:
The solution of the equation 3(3x - 10) = 5(x + 10) reveals that x = 20. Considering this equation defines the side length of an equilateral triangle, each side measures 50 units, and the total perimeter is 150 units.
Step-by-step explanation:
The student is asking for help with solving an equation related to the perimeter of an equilateral triangle. To solve the equation 3(3x - 10) = 5(x + 10), we must first distribute the 3 on the left-hand side and then simplify both sides of the equation.
Performing distribution and simplification, we get:
Then we move the variables to one side and the constants to the other:
Next, we divide by 4 to solve for x:
If the equation was meant to represent the perimeter of an equilateral triangle, then each side of the triangle would be 3x - 10 units long. Substituting x with 20,
- Side length = 3(20) - 10
- Side length = 60 - 10
- Side length = 50 units
The perimeter of an equilateral triangle is the sum of the lengths of all three sides, so:
- Perimeter = 3 × 50
- Perimeter = 150 units