Question

equilateral triangle abc has a perimeter of 96 millimeters. a perpendicular bisector is drawn from angle a to side bc at point m. what is the length of mc? 16 mm 24 mm 32 mm 48 mm

Explanation:

Step1: Find side - length of equilateral triangle

In an equilateral triangle, all sides are equal. Let the side - length of $\triangle ABC$ be $s$. The perimeter $P$ of an equilateral triangle is $P = 3s$. Given $P=96$ mm, then $3s = 96$, so $s=\frac{96}{3}=32$ mm.

Step2: Use property of perpendicular bisector in equilateral triangle

In an equilateral triangle, a perpendicular bisector from a vertex to the opposite side bisects that side. If $M$ is the point where the perpendicular bisector from $A$ to $BC$ intersects $BC$, and the length of $BC$ is $32$ mm, then $MC=\frac{BC}{2}$. Since $BC = 32$ mm, $MC = 16$ mm.

Answer:

16 mm