MATH SOLVE

4 months ago

Q:
# Triangle MRN is created when an equilateral triangle is folded in half. What is the value of y?A. 2β3 unitsB. 4 unitsC. 4β3 unitsD. 8 units

Accepted Solution

A:

we know thatIf Triangle MRN is created when an equilateral triangle is folded in halfthen[tex]RM=\frac{1}{2}*MN[/tex][tex]MN=6+2=8\ units[/tex]so[tex]RM=\frac{1}{2}*8=4\ units[/tex]Applying the Pythagorean Theorem in triangle MRN[tex]MN^{2}=NR^{2}+RM^{2}[/tex]we have [tex]MN=8\ units[/tex][tex]RM=x=4\ units[/tex][tex]NR=y[/tex]substitute[tex]8^{2}=y^{2}+4^{2}[/tex]solve for y[tex]y^{2}=8^{2}-4^{2}[/tex][tex]y^{2}=48[/tex][tex]y=\sqrt{48}=4\sqrt{3}\ units[/tex]thereforethe answer is the option C[tex]4\sqrt{3}\ units[/tex]