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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 135

Problem #1011 at projectEUREKA says:

"If the length of each side of a triangle is increased by 20%, then the area

of the triangle is increased by:"

Take a 3-4-5 triangle, increase each side by 20%

we get 3.6-4.8-6

which has an area of 8.64

8.64/6 = 1.44

I get 44% as the answer, but it says that's wrong.

It even says solution verified.

**The eclipses from Algol come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Hi;

They think it is 40%, that is weird, you have done yours right.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 135

Thanks for verifying this BobbyM,

I wasn't sure if I was losing my mind or not.

**The eclipses from Algol come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

You might be, It is just that we are losing it together. I am getting your answer. Is it possible for other than a right triangle that the answer would be 40% ?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Hi Fruityloop;

To prove that you are right we can use the general formula for the area of any triangle given 3 points.

A is for any 3 points and B is for those 3 points multiplied by a scaling factor that lengthens each side by 6 / 5. It is easy to see that you can manipulate B to:

C, B is just 36 / 25 times A. That is where the 1.44 = 36 / 25 comes from. You are right for any triangle.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Fruityloop****Member**- Registered: 2009-05-18
- Posts: 135

Here's another one: problem #996

A sum of 35 integers is S. Two digits in one of the integers are interchanged and a new sum T is produced. Then the difference S - T is necessarily divisible by:

They think the answer is 11.

Take the sum of the first 35 counting numbers...(35*36)/2 = 630.

Now switch 31 into 13 and add again and you end up with 612.

630-612 = 18 which is divisible by 3 and not 11.

**The eclipses from Algol come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Hi Fruityloop;

Agreed! I tried it with the series 50 + 51 + 52 + ,,, 84 and switched 81 into 18.

Have you been able to get to their explanations?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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