each edge of the cube is 6 cm. find the distance from the midpoint of one of the face diagonals to the furthest vertex of the cube.

Question

i just need help with this problem. there is a cube provided but i dont think it is needed

Answer 1

from the midpoint of the diagonal draw a line down perpendicular to the bottom edge

this measure is 3 cm and is one leg of a right triangle

the other leg is half the measure of the bottom edge which is also 3 cm

the hypotenuse of this triangle is half the measure of the diagonal

let "h" be this measure

h=√(9+9)

h=√9*2

h=3√2

this measure and the length of one edge are the legs of another right triangle whose hypotenuse is the distance from the midpoint of the face diagonal to the bottom furthest vertex

let d=this distance

d²=6²+(3√2)²

d²=36+18

d²=54

d=√54

d=3√6 cm