Questions: 2) = 12x + 9 4 - 10) = 3x^2 + 9x - 6

Find the perimeter.

Set up the equation

Since the triangle is equilateral, all sides are equal. Therefore, \(9x - 10 = x^2 + 4\) \(9x - 10 = 2x^2\)

Solve the first equation

\(x^2 - 9x + 14 = 0\) \((x - 2)(x - 7) = 0\) \(x = 2\) or \(x = 7\)

Solve the second equation

\(2x^2 - 9x + 10 = 0\) \(2x^2 - 4x - 5x + 10 = 0\) \(2x(x - 2) - 5(x - 2) = 0\) \((2x - 5)(x - 2) = 0\) \(x = 2\) or \(x = \frac{5}{2}\)

Find the common solution

The common solution is \(x = 2\).

Calculate the length of each side

If \(x = 2\), side length is \(9(2) - 10 = 8\) If \(x = 2\), side length is \(2(2^2) = 8\) If \(x = 2\), side length is \(2^2 + 4 = 8\)

Calculate the perimeter

Perimeter \(= 3 \times 8 = 24\)

\(\boxed{24}\)

24