Expert: Steve Holleran - 12/15/2007

Question
A city block 500 feet by 500 feet has a large building 300 feet by 400 feet in the NW corner.  The rest of the block is an unobstrucked paved lot.  What is the shortest distance from the SW corner to the NE corner of the city block, going through the paved lot-- to the bearest foot.
Pleas show me how you got the answer.
Thank you
S

Answer
Hi Sandi,

Okay, you have a diagram like this (I didn't put in the lines--you can do that easy enough.  Its really difficult to draw stuff on this site).

  C                     D         E




  B                     G  



  A                              F

You want to go from A to E, and you have the following:

AB = 200         BC = 300

CD = 400         DE = 100

EF = 500         FA = 500

BG = 400

Okay, the shortest path would be from A to G to E.

Now look at triangle ABG :  the legs are 200 and 400, so

  AG^2 = 200^2 + 400^2 = 40000 + 160000 = 200000

so  AG = sqrt(200000) = 447.2

On triangle GDE, you have legs 300 and 100, so

  GE^2 = 300^2 + 100^2 = 90000 + 10000 = 100000

so  GE = sqrt(100000) = 316.2
Then the total is 447.2 + 316.2 = 763.4 = 763 ft.

Hope this helps .

Steve