Question

Geometry help please?!

Equilateral triangle XYZ is cut in half by line segment XP where point p is the midpoint of YZ. If XY=6, what is the length of XP?
A) 6 √2
B) 3 √3
C) 3 √2
D) 4
E) 3

Answer 1

Firstly , we can draw diagram

we are given that

XYZ is equilateral triangle

so,

XY=YZ=XZ=6

and when we draw a line from X intersect at mid point between Y and Z

It will also be perpendicular line

so, we can use Pythagoras theorem

$6^2=h^2+3^2$

now, we can solve for h

$h^2=27$

$h=3\sqrt{3}$

so,

$XP=3\sqrt{3}$..............Answer