Yes I know basic math. Can you provide any useful information or are you just going to be mean?

If we are following the Pythagorean theorem, A^2 + B^2 = C^2, then you are expecting me to believe that 1^2 + 3^2 = 3^2 (because we know for certain that the hypotenuse is 3), when it clearly equals 10.

Edit: it is clear to me that we are not at all on the same page.

Michael2_3B, I am definitely not the smartest person on this website but here is my reasoning for how Sam got his answer: you add the 3 by 3 square in the middle of the larger square with the 4 other triangles that come together with the smaller square to form a larger, rotated square. each of the 4 triangles is obviously (1*3)/2 sq in = 1.5 sq inches, so multiply that by 4 and you have 6 square inches. add that to the 3 by 3 square (which is 9 sq in), and you have 15 sq inches.

The height of a triangle isn't necessarily the edge length - it's the perpendicular distance from the base edge to the intersection point of the other two.


So, the base here has length 3, and the corresponding height is 1, for a total area of 3*1/2 = 1.5. Multiply that by four, add the square, which is 9, to get a total area of 15.

Somebody please tell me the lengths of these 2 sides, with the blue question marks.



And do not say 1 and 3, that is impossible.

The length of the sides doesn't freaking matter when you are trying to find the area of a triangle.

The math finally computed for me. My apologies. Let's forget this happened

Massive brain fart moment: I forgot that there was more than one way to label the base and height of the triangle, thus the massive confusion on my part. I was thinking the only way to get the area is to get the side lengths first.

You really don't need to know the length of those sides, but I calculated them anyways:

Let's call the short side a, and the long side b.
We'll also call the shorter subsection of the line with length 3 d, leaving the other section with length 3-d.
We thus obtain this system of equations:

Code:

Plug'n'chugg'n into Wolfram|Alpha yields a = √(3/2 (3-√5)) and b = √(3/2 (3+√5)). Multiplying these together and dividing by 2 also gives an area of 1.5.

My English class spent about 15 minutes every day for an entire week debating how many holes a straw has (obviously only one- how many holes does a donut have?) and the related problem of how many holes a t-shirt has (three). In my opinion, this isn't really a math problem, just a language problem. The main issue being that people conflate the idea of an opening with a hole. My English teacher, however, disagreed- anything that takes time out of her class clearly isn't English

Here's a nice geometric puzzle, recreated faithfully in google sheets.


Rearrange the 6 L-shaped pieces on the right so that they fit on the 5x5 board on the left, with the hole being in a different location (i.e. not in the center of the square).

Surely that would depend on the context or something? Let's say you take that straw and put it underground, and put the two ends sticking out of the ground in separate locations. There are, what appear to be, 2 holes. But then again, it is indeed a language problem.

Edit: Solved.
Do not click this if you want to solve the L puzzle yourself!

Here's my solution, too lazy to generate a graphic for it:
acddd
acccd
aafee
fffbe
*bbbe

Guess I'll contribute one too - this is more of a thought puzzle, rather than a problem with a defined solution.

The difficulty of the Bitcoin network is adjusted so that, on average, a new block gets added every ten minutes. Because being able to add a block is essentially dependent on a lucky guess, even if it's been a very long time since the last block, the average time from now until the next block is still ten minutes. So, for any time t, the expected time the next block will be added is t + 10. Likewise, the expected time for the previous block is t - 10. So, the expected amount of time between the previous block and the next block is (t + 10) - (t - 10) = 20 minutes. But the expected amount of time between any block and the next one was defined to be 10 minutes. How can this be?

There is actually an entire branch of mathematics dedicated to answering questions like that one, so I would say it is a math problem. See topology. In a topological sense, a straw has one hole, and is topologically identical to a single-handled mug.