Calculate the perimeter of the isosceles triangle of the figure, knowing that § = 45° Measurement of the AC side = x2 - 4 meters Measurement of the BC side = 3x meters

To calculate the perimeter of the isosceles triangle, we need to find the lengths of all three sides and add them together. Given that § (angle) is 45°, we know that the triangle is an isosceles right triangle. Let's calculate the lengths of the sides: AC = x^2 - 4 meters BC = 3x meters Since it is an isosceles right triangle, AC and BC are equal: AC = BC Therefore, we can set up the equation: x^2 - 4 = 3x Rearranging the equation: x^2 - 3x - 4 = 0 Now we can solve this quadratic equation. Factoring or using the quadratic formula, we find that the solutions are x = -1 and x = 4. Since lengths cannot be negative, we take x = 4 as the valid solution. AC = 4^2 - 4 = 12 meters BC = 3 * 4 = 12 meters Now, we can calculate the perimeter by adding the lengths of all three sides: Perimeter = AC + BC + AC = 12 + 12 + 12 = 36 meters Therefore, the perimeter of the isosceles triangle is 36 meters.