The perimeter of triangle ABC, with sides AB, AC, and BC, is 60 units. The right-angled triangle has a perpendicular drawn from A to BC, creating a 3-4-5 triangle.
Correct option is option C.
To find the perimeter of triangle ABC, we need to sum the lengths of its three sides, AB, AC, and BC.
Given:
AB = 20
AC = 15
DB = 10
We also know that a perpendicular is drawn from A to the line BC, marking the point as D, and ∠D = 90 degrees.
The length of BC can be calculated using the Pythagorean theorem since triangle ABC is a right-angled triangle:
BC = √(AB^2 + AC^2)
Substitute the given values:
BC = √(20^2 + 15^2) = √(400 + 225) = √625 = 25
Now, we can find the perimeter:
Perimeter = AB + AC + BC = 20 + 15 + 25 = 60
Therefore, the correct answer is 60. The perimeter of triangle ABC is 60 units making option C the correct option.