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

An equilateral triangle have all its three sides to be congruent.

The value of x is 4

From the question (see attachment), we have the following observations.

Given that:

Side length MR is then calculated as:

So, we have:

Also:

So, we have:

Hence, the value of x is 4

Read more about equilateral triangles at:

link

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b