Question

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

A. 2√3 units
B. 4 units
C. 4√3 units
D. 8 units

Answer 1

The correct option is C.

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. The side length of the triangle is

`MO=NO=MN=MS+SN=2+6=8`

Since NR is a perpendicular bisector, therefore

`RM=(MO)/(2)=(8)/(2)=4`

Using Pythagoras property in triangle MNR,

`MR^2+NR^2=MN^2`

`4^2+y^2=8^2`

`y^2=64-16`

`y=√(48)`

`y=4√(3)`

Therefore option C is correct.

Answer 2

we know that

If Triangle MRN is created when an equilateral triangle is folded in half

then

`RM=(1)/(2)*MN`

`MN=6+2=8\ units`

so

`RM=(1)/(2)*8=4\ units`

Applying the Pythagorean Theorem in triangle MRN

`MN^(2)=NR^(2)+RM^(2)`

we have

`MN=8\ units`

`RM=x=4\ units`

`NR=y`

substitute

`8^(2)=y^(2)+4^(2)`

solve for y

`y^(2)=8^(2)-4^(2)`

`y^(2)=48`

`y=√(48)=4√(3)\ units`

therefore

the answer is the option C

`4√(3)\ units`