## Poll

 I love math! 8 votes (47.05%) Math is great. 6 votes (35.29%) My religion is mathology. 3 votes (17.64%) Women didn't speak to me until I was 30. 2 votes (11.76%) Total eclipse reminder -- 04/08/2024 6 votes (35.29%) I steal cutlery from restaurants. 2 votes (11.76%) I should just say what's on my mind. 3 votes (17.64%) Who makes up these awful names for pandas? 2 votes (11.76%) I like to touch my face. 8 votes (47.05%) Pork chops and apple sauce. 6 votes (35.29%)

17 members have voted

ksdjdj Joined: Oct 20, 2013
• Posts: 894
March 29th, 2020 at 9:02:15 PM permalink
Quote: Wizard

(snip)
A 3-4-5 triangle is inscribed in a square of length x.

Find x.

Pen or pencil, grid paper (cm*** markings/spacing), ruler (cm*** markings/spacing) and a math compass
but there is probably an "easier/better" way^^^
***:
As long as the grid paper markings and ruler markings are the same, then you can use any unit of measurement, eg inches, mm, etc...

^^^:
Surely the Wiz doesn't expect us to have all this equipment lying around, to solve an "easier than normal" problem, so there must be a better way (I just can't think of it).

was I at least correct that this is the equipment needed for one way of getting the answer/ approximate answer (or am I wrong?)
Wizard Joined: Oct 14, 2009
• Posts: 22082
Thanks for this post from: March 29th, 2020 at 9:13:18 PM permalink

Graph paper would certainly be useful to get an estimate, but for full credit, I want to see an algebraic solution.
It's not whether you win or lose; it's whether or not you had a good bet.
ssho88 Joined: Oct 16, 2011
• Posts: 453
March 29th, 2020 at 10:07:21 PM permalink

See image : https://imge.to/i/yV3aUG

From blue triangle, cos(θ) = x/4,

and

From red triangle, cos(θ) = a/3

Therefore, a/3= x/4, a=3x/4, and b = x/4

b^2+x^2 = 4^2

(x/4)^2 + x^2 = 16

x= 16/(17)^0.5 = 3.8806

ksdjdj Joined: Oct 20, 2013
• Posts: 894
March 29th, 2020 at 10:09:21 PM permalink

Note: I know that this formula works for at least one type of "area of a triangle inside a square " problem, but I don't know if it works for the type you posted.

Length of side "X" = Square root of the "area of the square" =
Square root of ("Area of the Triangle" x 2)

Using the above, for a triangle where: 3 = base and 4 = height , then X would be = 3.46... (or square root of 12 to be exact).

X = √ 12 (where X must be a positive number )

I hope this is correct, as I will not be attempting any more answers to this problem if it is wrong (in other words, "too hard for me")

Edit:
Going by the answer above by ssho88, I am going to say my answer is almost certainly wrong.
Last edited by: ksdjdj on Mar 29, 2020
gordonm888 Joined: Feb 18, 2015
• Posts: 2610
Thanks for this post from: March 29th, 2020 at 11:58:04 PM permalink
Let's hope there is not a pandemic lockdown during the next total eclipse in 2024.
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
charliepatrick Joined: Jun 17, 2011
• Posts: 2146
March 30th, 2020 at 2:19:15 AM permalink
Quote: Wizard

Here is your next puzzle that is too simple to be beer-worthy, but is nevertheless pretty challenging. A 3-4-5 triangle is inscribed in a square of length x.

Find x.

Nice puzzle - thanks.
The angle of the 3-4-5 triangle is a right angle, so the angle of the blue triangle at 34 and the red triangle add up to 90. So the blue triangle and red triangle are similar.
Thus if the base of blue is x, the base of red is 3/4 x. So the side of blue is 1/4x.
(Academically you can now work your way round to show the all parts clockwise are x 1/4x 3/4x 3/16x 13/16x x.)

Looking at blue triangle x^2 + (1/4 x)^2 = 16 = 17/16 x^2. So x^2 = 256/17.

If you do the same maths with the others you get the same result (e.g. 25 = (169+256)/256 x^2 = 425/256 x^2).

X = SQRT (256/17).
Wizard Joined: Oct 14, 2009
• Posts: 22082
March 30th, 2020 at 6:46:47 AM permalink
Congratulation to ssho88 and Charlie for a correct answer!
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard Joined: Oct 14, 2009
• Posts: 22082
March 30th, 2020 at 6:47:08 AM permalink
Quote: gordonm888

Let's hope there is not a pandemic lockdown during the next total eclipse in 2024.

Amen to that.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard Joined: Oct 14, 2009
• Posts: 22082
March 30th, 2020 at 6:57:12 AM permalink 