triangle mrn is created when an equilateral triangle is folded in half. what is the value of y? o 2√3 units…

Explanation:

Step1: Analyze the equilateral - triangle property

When an equilateral triangle is folded in half, triangle MRN is a right - triangle. Let the side length of the original equilateral triangle be (a). In right - triangle MRN, assume the hypotenuse (MN = a), and if we consider the relationships in the right - triangle formed by folding. Let's use the Pythagorean theorem. First, note that if we assume some side - length relationships based on the folding of the equilateral triangle. Let's assume the original equilateral triangle has side length (8) (by observing the given values and the nature of the problem). When folded in half, in right - triangle MRN, (MN = 8), (MS=2), so (SN=MN - MS=8 - 2 = 6).

Step2: Apply the Pythagorean theorem

In right - triangle RSN, if we assume (RN = y), (SN = 6), and assume the right - angle is at (R). According to the Pythagorean theorem (RN^{2}+RS^{2}=SN^{2}). In an equilateral triangle folded in half, we can also use the fact that the height of an equilateral triangle (h=\frac{\sqrt{3}}{2}s) (where (s) is the side - length of the equilateral triangle). In right - triangle MRN, if we assume the side - length of the original equilateral triangle is (8), and using the Pythagorean theorem in right - triangle MRN with (MN = 8) and (MR=\frac{8}{2}=4). By the Pythagorean theorem (y=\sqrt{MN^{2}-MR^{2}}). Since (MN = 8) and (MR = 4), we have (y=\sqrt{8^{2}-4^{2}}=\sqrt{64 - 16}=\sqrt{48}=4\sqrt{3}).

Answer:

(4\sqrt{3}) units