## Poll

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**43 members have voted**

March 29th, 2020 at 9:02:15 PM
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Quote:Wizard

(snip)

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

Find x.

Could I possibly find an answer or approximate answer if I had:

Pen or pencil, grid paper (cm*** markings/spacing), ruler (cm*** markings/spacing) and a math compass

***:

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?)

March 29th, 2020 at 9:13:18 PM
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Graph paper would certainly be useful to get an estimate, but for full credit, I want to see an algebraic solution.

“Extraordinary claims require extraordinary evidence.” -- Carl Sagan

March 29th, 2020 at 10:07:21 PM
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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

March 29th, 2020 at 10:09:21 PM
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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

March 29th, 2020 at 11:58:04 PM
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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, are dead. And a thousand thousand slimy things live on, and so do I.

March 30th, 2020 at 2:19:15 AM
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Nice puzzle - thanks.Quote:WizardHere 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.

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).

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).

March 30th, 2020 at 6:46:47 AM
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Congratulation to ssho88 and Charlie for a correct answer!

“Extraordinary claims require extraordinary evidence.” -- Carl Sagan

March 30th, 2020 at 6:47:08 AM
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Quote:gordonm888Let's hope there is not a pandemic lockdown during the next total eclipse in 2024.

Amen to that.

“Extraordinary claims require extraordinary evidence.” -- Carl Sagan

March 30th, 2020 at 6:57:12 AM
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Here is your next problem.

The state of Denial has a population of 20 million. They are in the early states of an epidemic. They estimate one person in 500 will need to be on a ventilator when the epidemic is at its peak. How many ventilators should they have on hand to have a 95% chance of having enough?

The state of Denial has a population of 20 million. They are in the early states of an epidemic. They estimate one person in 500 will need to be on a ventilator when the epidemic is at its peak. How many ventilators should they have on hand to have a 95% chance of having enough?

Last edited by: Wizard on Mar 30, 2020

“Extraordinary claims require extraordinary evidence.” -- Carl Sagan