Determine the perimeter of triangle ABC if A (4; 0) B (7; 4) C (-4; 6)

Find the lengths of sides A and B by the formula:

| AB | = sqrt [(x_B – x_A) ^ 2 + (y_B – y_A) ^ 2] = sqrt [(7 – 4) ^ 2 + (4 – 0) ^ 2] = sqrt (3 ^ 2 + 4 ^ 2) = five.

Similarly, we find the lengths of the sides BC and AC:

| BC | = sqrt [(x_C – x_B) ^ 2 + (y_C – y_B) ^ 2] = sqrt [(- 4 – 7) ^ 2 + (6 – 4) ^ 2] = sqrt (11 ^ 2 + 2 ^ 2) = sqrt (125) = 5 * sqrt (5);

| AC | = sqrt [(x_C – x_A) ^ 2 + (y_C – y_A) ^ 2] = sqrt [(- 4 – 4) ^ 2 + (6 – 0) ^ 2] = sqrt (8 ^ 2 + 6 ^ 2) = 10.

Then the perimeter of the triangle is

P = | AB | + | BC | + | AC | = 5 + 5 * sqrt (5) + 10 = 15 + 5 * sqrt (5).