Triangle MRN is created when an equilateral triangle is folded in half. Triangle N R M is shown. Angle N R M is a right angle. A

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Triangle MRN is created when an equilateral triangle is folded in half. Triangle N R M is shown. Angle N R M is a right angle. A

n altitude is drawn from point R to point S on side M N to form a right angle. The length of N S is 6, the length of S M is 2, the length of R M is x, the length of N R is y, and the length of R S is z. What is the value of x? 2 StartRoot 3 EndRoot units 4 units 4 StartRoot 3 EndRoot units 8 units

Mathematics

2 answers:

Fed [463] · Answer 1 · 2023-12-18T15:51:09+03:00

Answer:

The value of x is 4.

Step-by-step explanation:

It is given that triangle MRN is created when an equilateral triangle is folded in half.

It means original equilateral is triangle MNO and NR is a perpendicular bisector (<em>A line which cuts a line segment into two equal parts at 90°</em>).

The side length of the triangle is

NO = NS + SM = 6 + 2 = 8

Since an equilateral triangle is a triangle in which all three sides are equal and NR is a perpendicular bisector, therefore

RM = MO/2 = 8/2 = 4

The value of x is 4.