SOLUTION: Hey, thankyou for the help..The question is_ a open carboard measures a base of 3m x 1m and has a height of 3m. a spider in corner A moves across the surface of box to point B.

Algebra ->  Length-and-distance -> SOLUTION: Hey, thankyou for the help..The question is_ a open carboard measures a base of 3m x 1m and has a height of 3m. a spider in corner A moves across the surface of box to point B.      Log On


   

Question 207268: Hey, thankyou for the help..The question is_
a open carboard measures a base of 3m x 1m and has a height of 3m. a spider in
corner A moves across the surface of box to point B. Wnat is teh SHORTEST distance that the spider cab travell between A and B. Imagine 3-D cube i.e. like normall room. Sorry for the ammuture drawing was limited.
_____________*A
/ /
/ /
/____________/

3m /
/ 1m
_____________/
*B 3m
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The shortest distance between two points is a straight line and in this case, it's the diagonal that runs from corner to corner. I'm assuming that the spider is traveling from an upper corner to a bottom corner (or vice versa).


It turns out that the diagonal 'd' can be found by the formula


a%5E2%2Bb%5E2%2Bc%5E2=d%5E2 where 'a', 'b', and 'c' are the lengths of the box.


Note: this is analogous to the Pythagorean Theorem.



So in this case, a=3, b=1, and c=3 giving us the equation


3%5E2%2B1%5E2%2B3%5E2=d%5E2


9%2B1%2B9=d%5E2 Square each value


19=d%5E2 Combine like terms.


d=sqrt%2819%29 Take the square root of both sides. Note: we're only considering the positive square root.


d=4.359 Approximate the square root.


So the shortest distance that the spider can travel from A to B is roughly 4.359 meters.