# Shortest distance question

• Oct 5th 2006, 05:49 AM
chickenwing
Shortest distance question
I can't figure out what formula to use to solve this

A city block 500 feet by 500 feet is an unobstructed paved lot, except for a small office building 100 feet by 100 feet, centered in the middle of the block. What's the shortest distance from the SW corner to the NE corner, going through the paved lot and along (but not through) the building (to the nearest foot)?
• Oct 5th 2006, 05:59 AM
topsquark
Quote:

Originally Posted by chickenwing
I can't figure out what formula to use to solve this

A city block 500 feet by 500 feet is an unobstructed paved lot, except for a small office building 100 feet by 100 feet, centered in the middle of the block. What's the shortest distance from the SW corner to the NE corner, going through the paved lot and along (but not through) the building (to the nearest foot)?

Without using Calculus I can't prove its the shortest path, but what you need to do is walk a straight line from the SW corner of the lot to the SE corner of the building, then to the NE corner of the lot. Alternately you could go from the SW corner of the lot to the NW corner of the building, then to the NE corner of the lot.

Since all the paths are straight lines you can use the Pythagorean Theorem to figure out each distance.

-Dan
• Oct 5th 2006, 07:21 AM
ThePerfectHacker
Quote:

Originally Posted by topsquark
Without using Calculus I can't prove its the shortest path, but what you need to do is walk a straight line from the SW corner of the lot to the SE corner of the building, then to the NE corner of the lot. Alternately you could go from the SW corner of the lot to the NW corner of the building, then to the NE corner of the lot.

Since all the paths are straight lines you can use the Pythagorean Theorem to figure out each distance.

-Dan

I think I do not understand what you are saying or what the problem is saying.
The shortest distance is,
• Oct 5th 2006, 07:42 AM
topsquark
Quote:

Originally Posted by ThePerfectHacker
I think I do not understand what you are saying or what the problem is saying.
The shortest distance is,

This is a good point. I had assumed the target was the NE corner of the lot.

However, there is a shorter path on your diagram as well. SW corner of the lot to the NW corner of the building. Then to the NE corner of the building.

-Dan
• Oct 5th 2006, 08:41 AM
CaptainBlack
Quote:

Originally Posted by topsquark
This is a good point. I had assumed the target was the NE corner of the lot.

However, there is a shorter path on your diagram as well. SW corner of the lot to the NW corner of the building. Then to the NE corner of the building.

-Dan

Since the terms "SW corner" and "NE corner" are not qualified in any way
they should be assumed to be of the same entity; either the lot or the
building.

So the natural interpretation is Topsquarks, or the much less plausible distance
from one corner of the building to the opposite one taking a path around
the outside of the building (that is 200 ft)

RonL
• Oct 5th 2006, 11:57 AM
chickenwing
Quote:

Originally Posted by ThePerfectHacker
I think I do not understand what you are saying or what the problem is saying.
The shortest distance is,

I think they want from the SW corner of the big lot to the the NE corner of the big lot; since they don't want you to cut acroos diagonally from corner to corner, I think the shortest way would be this: (I attached a file with a diagram) but how do I find the measurements?
• Oct 5th 2006, 01:27 PM
earboth
Quote:

Originally Posted by chickenwing
I can't figure out what formula to use to solve this

A city block 500 feet by 500 feet is an unobstructed paved lot, except for a small office building 100 feet by 100 feet, centered in the middle of the block. What's the shortest distance from the SW corner to the NE corner, going through the paved lot and along (but not through) the building (to the nearest foot)?

Hi,

I've attached a diagram to show which distances I've calculated.

The total distance is: d = 2*sqrt(200² + 300²) ≈ 721 feet

tschüss

EB