#1 (permalink)

For my study guide for my geometry final, our teacher gave us a bunch of problems. I figured out all but three. Here they are. Please help!

1. A box is 6in in length, 5in in width, and 6in high. If a spider is in the top right front corner of the box and a fly is opposite bottom left rear corner, what is the shortest path necessary for the spider to walk, and how far will it walk? (The answer is not 13 inches)

2. Another spider walked straight for 6 inches, made a 90 degree turn to the right, walked 6 more inches, made another 90 degree turn to the right, walked another 6 inches and ended up exactly where he started. how can this be?

4. A cattle farmer has 1000m of fnecing and wants to fence in the largest pasture he can. he gives the problems to his sons, Harry and David. Harry's solution to the problem is to use the rectangular formula A=bh, and find the largest A where 2L+2W=1000
a) What are the dimensions of Bobby's Pasture
b) David's solution was, of course, more brilliant and resulted in a pasture that was 25% larger. How did he accomplish such a feat.

I greatly appreciate any help. My final is tomorrow so please help tonight!

#2 (permalink)

1. If you flatten the box into a flat plane you end up with a 12 by 5 rectangle, and if the spider walks a beeline diagonally across this rectangle, then using the Pythagorean Theorem, he only walks 13 inches. Nice and even right? Well, dozens of people have written in saying the answer is wrong. The flattened box could also create an 11 by 6 triangle which has a hypotenuse of 12.53 inches. Note the following illustration:

2. The spider is walking on a ball. On a flat plane a triangle can only have 180 degrees, but on a curved surface, it can have more. Think of a plane flying over the Earth from the north pole to the Equator then turns right and follows the equator to 90 degrees longitude, then turns right again and heads to the north pole, you have circumscribed a triangle with 270 degrees total.


4. Harry's solution is a square pasture, 250m per side, with a pasture area of 62,500sq. m. David's solution is to make a round pasture with a circumference of 1000m resulting in a pasture area of 79577.47sq. m.

Source: http://members.cox.net/mathmistakes/answers.htm#g1

#3 (permalink)

LOL.. Trust him, he knows.

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#4 (permalink)

LOL... Trust him, he knows.

#5 (permalink)

Thanks people (sarcastically and not lol), but I copied and pasted that from the internet (removed quote since I had to change some minor parts). I hate geometry. :/