Question

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

Answer 1

Answer:

The correct option is C.

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. The side length of the triangle is

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

Since NR is a perpendicular bisector, therefore

$RM=\frac{MO}{2}=\frac{8}{2}=4$

Using Pythagoras property in triangle MNR,

$MR^2+NR^2=MN^2$

$4^2+y^2=8^2$

$y^2=64-16$

$y=\sqrt{48}$

$y=4\sqrt{3}$

Therefore option C is correct.

Answer 2

we know that

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

then

$RM=\frac{1}{2}*MN$

$MN=6+2=8\ units$

so

$RM=\frac{1}{2}*8=4\ units$

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

$y^{2}=8^{2}-4^{2}$

$y^{2}=48$

$y=\sqrt{48}=4\sqrt{3}\ units$

therefore

the answer is the option C

$4\sqrt{3}\ units$