The perimeter of the isosceles triangle is C) 32 units.
Explanation:
Step 1; First, we plot the three ends of the triangle. Assume the bottom left is A, the bottom right is B and the top end is C. The coordinates are;
A = (-6, -2), B = (6, -2) and = C (0, 6). A triangle's perimeter is the sum of its three side lengths. So we need to determine the side lengths of the given sides.
Step 2; To find the distance between A (-6, -2) and B (6, -2), we use the formula
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between (-6, -2) and (6, -2) where (-6, -2) is (x1, y1) and (6, -2) is (x2, y2).
Distance = √ (6 - (-6))² + (2 - (-2))² = √ 12² + 0² = √12² = 12 units.
Step 3; To find the distance between C (0, 6) and B (6, -2), we use the formula
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between (0, 6) and (6, -2) where (0, 6) is (x1, y1) and (6, -2) is (x2, y2).
Distance = √ (6 - 0)² + (-2 - 6)² = √ 6² + 8² = √36 + 64 =√100 = 10 units.
Step 4; To find the distance between C (0, 6) and A (-6, -2), we use the formula
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between (0, 6) and (-6, -2) where (0, 6) is (x1, y1) and (-6, -2) is (x2, y2).
Distance = √ (-6 - 0)² + (-2 - 6)² = √ 6² + 8² = √36 + 64 =√100 = 10 units.
Step 5; The perimeter of the triangle = 12 + 10 + 10 = 32 units, which is option C.