In the figure below, points A, B, and C are collinear, and AB and BC are each 6 units long. If the area of �ACD is 24 square units, how many units long is the altitude BD?
A. 2
B. 4
C. 6
D. 8
E. 12
Are the points (4,-12), (6, -3) and (12, 24) collinear
To find the length of the altitude BD, we can use the formula for the area of a triangle.
Given that points A, B, and C are collinear, we have an isosceles triangle ABC, where AB = BC = 6 units. The base of the triangle is AC, and the height or altitude is BD.
The area of a triangle can be calculated using the formula: Area = (base * height) / 2.
We are given that the area of triangle ACD is 24 square units. The base AC is equal to AB + BC, which is 6 + 6 = 12 units.
Plugging these values into the formula, we have:
24 = (12 * BD) / 2
Simplifying the equation, we get:
24 = 6 * BD
Dividing both sides by 6, we find:
BD = 4
Therefore, the length of the altitude BD is 4 units.
The answer is B: 4.