Question 1151111: In the diagram below, point X is the intersection of the two diagonals TW and UV of the cubical box illustrated. The shortest distance from point T to point Z is 4 sqrt3 cm. Find the area in cm2, of triangle XYZ.
Diagram: https://imgur.com/a/ciK5pIK
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
TZ is the space diagonal of the cube. Given its length as 4*sqrt(3), the side of the cube has length 4.
Picture points A and B as the midpoints of VW and YZ, respectively. Then AB=4, AX=2, and BX is the altitude of triangle XYZ.
Use the Pythagorean Theorem to find the length of altitude BX; then the area of triangle XYZ is one-half base times height....
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