What is the perimeter of the isosceles triangle shown below?
A) 27 units
B) 22 units
C) 32 units
D) 24 units

The perimeter of the isosceles triangle is C) 32 units.

Step-by-step 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.

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