Question

The perimeter of the equilateral triangle $△ABC$ is 12 inches. If PC is a median of the triangle, find the length PB.

• A. 2
• B. 4 inches
• C. 2 inches

Answer 1

The correct option is C 2 inches

An equilateral triangle has equal sides.
Let one side is $a$ inches.
$\therefore$ Perimeter = sum of all the sides of the triangle
$=a+a+a$ inches
$\Rightarrow 12$ inches $=3a$ inches
$\Rightarrow a=\frac{12}{3}=4$ inches.
$\therefore$ Each side is $4$ inches.

Median is a line from a vertex of a triangle to the midpoint of its opposite side.

Here, PC is the median that passes through vertex C and the midpoint of AB.
$\therefore$ P is the midpoint of AB.

Hence, Length of PB $=\frac{\text{length of AQ}}{2}$
$=\frac{4}{2}$ inches
$=2$ inches