Question

triangle mrn is created when an equilateral triangle is folded in half. what is the value of x?
2\sqrt{3} units
4 units
4\sqrt{3} units
8 units

Explanation:

Step1: Find full side length of equilateral triangle

The segment NS = 6, SM = 2, so the side length of the original equilateral triangle is $6 + 2 = 8$. Since $\triangle MRN$ is half of the equilateral triangle, $NM = 8$, and $x$ is half of the base of the equilateral triangle.

Step2: Calculate x using triangle properties

In an equilateral triangle, all sides are equal. When folded in half, the base of $\triangle MRN$ (side $RM = x$) is half the side length of the original equilateral triangle.
$x = \frac{8}{2} = 4$

Answer:

4 units