Question

triangle ABC has AB=12, BC = 16, and AC = 20. IF D is on AC such that AD = 12, find area of triangle ABD

Answer 1

The area is
`32√(5)` or 71.5542 units²

Explanation:

Segment AD is a 12 units, and so is segment AB. This makes triangle ABD and isosceles triangle (a triangle with 2 equal side lengths)

The equation for area of an isosceles triangle given only the base and a side length s is

`A = (1)/(2) b \sqrt{s^2-(b^2)/(4) } \\`

`A = (1)/(2) * 16 * \sqrt{12^2-(16^2)/(4) } \\A = 8 * √(144-64) \\A = 8√(80) \\A = 32√(5)`

The area of Triangle ABD is
`32√(5)` units², or 71.5542 units² in decimal form.

Answer 2

To find the area of triangle ABD, we can use the formula for the area of a triangle: A = (1/2)bh, where b is the base of the triangle and h is the height.

First, we need to find the length of BD. We can use the Pythagorean theorem to do this:

BD^2 = AB^2 - AD^2

BD^2 = 12^2 - 12^2

BD^2 = 144 - 144

BD^2 = 0

BD = 0

This means that D is actually the midpoint of AC, and BD is a height of triangle ABD.

So, the base of triangle ABD is AB = 12, and the height is BD = 0. Therefore, the area of triangle ABD is:

A = (1/2)bh

A = (1/2)(12)(0)

A = 0

The area of triangle ABD is 0 because BD, the height of the triangle, is 0.