Given the regular triangle, ABC above, where AD bisects BC and BD = 16.2 meters, find the perimeter of ABC. Be sure to select the correct units.

Question
Answer:
In a regular triangle (also known as an equilateral triangle), all sides are of equal length. Since AD bisects BC, it means that BD and CD are equal, making AD the perpendicular bisector of BC. Let's denote the length of side AD as "x" meters. Since BD is 16.2 meters, CD is also 16.2 meters, and we have a right triangle BCD with BD = CD = 16.2 meters and AD = x meters. Now, we can use the Pythagorean theorem to find the length of AD (x): $$BD^2 = AD^2 + CD^2$$ $$16.2^2 = x^2 + 16.2^2$$ $$262.44 = x^2 + 262.44$$ Now, subtract 262.44 from both sides: $$x^2 = 0$$ Take the square root of both sides: $$x = 0$$ So, AD is 0 meters. This means that the triangle ABC is actually a line segment, not a triangle, and its perimeter is equal to the length of BD: Perimeter of ABC = BD = 16.2 meters. So, the perimeter of line segment ABC is 16.2 meters.
solved
general 6 months ago 1121