Question

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. An 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

Answer 1

MN = NS + SM = 6 + 2 = 8. In a right triangle, the foot of the altitude to the hypotenuse gives the relation RM^2 = MN · SM. So

RM^2 = 8 · 2 = 16, hence RM = 4.

Answer: 4 units.