Triangle MRN is created when an equilateral triangle is folded in half. What is the value of y?

Solution:

Given, the triangle MRN is created when an equilateral triangle is folded in half.

This implies the original equilateral triangle is MNO and NR is a perpendicular bisector.

The side length of the triangle is 

MO = NO = MN = MS + SN

= 6 + 2

= 8

Since NR is a perpendicular bisector, 

RM = Mo/2 

= 8/2 

RM = 4

Using Pythagoras theorem in triangle MNR,

MR² + NR² = MN²

(4)² + y² = (8)²

16 + y² = 64

y² = 64 - 16

y² = 48

Taking square root,

y = √48

y = 4√3 units

Therefore, the value of y is 4√3 units.

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Triangle MRN is created when an equilateral triangle is folded in half. What is the value of y?

Summary:

Triangle MRN is created when an equilateral triangle is folded in half. The value of y is 4√3 units.