Lenny Conundrum 199

[Jerch]

The Petpet Supplies shop is 655 metres from the Smoothie Store, 393 Metres from the Defence Magic shop, and 314 metres from the Grooming Parlour. The Defence Magic shop is 236 metres from the Grooming Parlour and 524 metres from the Smoothie Store.

Assuming the distance between the Grooming Parlour and the Smoothie Store is less than the distance between the Petpet Supplies shop and the Smoothie Store, what is the distance between the Grooming Parlour and the Smoothie Store? Please round to the nearest metre.

Maths. again...

I'd suggest taking a look at the bazaar... then by using 2 simple laws/theorems, and a good calculator (preferably graphing ones), you'd get your answer. It should take less than 5 min.

That is, if I got mine right...

[Kenjiro]

It took more than five minutes for me... But then again it's been quite a while since I last did math

Thanks for the tip about the bazaar. It would've been a lot harder if I didn;t have a visual to work with...

[mayootjuh]

You are sure that with that calculation you are benaeth 314?
I usted also 2 theorems/laws but is more then 314 with that.

[Jerch]

You are sure that with that calculation you are benaeth 314?
I usted also 2 theorems/laws but is more then 314 with that.

what's wrong with it being below/over 314 though :S??

[Kenjiro]

You are sure that with that calculation you are benaeth 314?
I usted also 2 theorems/laws but is more then 314 with that.

Actually, it says that the distance between the Grooming Parlour and the Smoothie Store is less than the distance between the Petpet Supplies shop and the Smoothie Store. In other words, it's less than 655

[Mongrel]

I didn't do any fancy calculations, but I also wound up with two different answers. I went with the lower one.

[Jerch]

It can't be less than 341 anyway....triangular inequality...

[Shadow_Twisted]

OK, for those who are confused:

Two triangles!

For those that still don't get it:

You have four points and a couple of distances between them. Which means, if you connect the dots, you can make two triangles with a mystery value for one of the sides.

You can double-check your answer because the equation to find it applies to BOTH triangles. The answers I got had about a .2 difference between each other, but they both rounded up.

Equation: A squared + B squared = C squared

Should look familiar to you, Pythagorean Theorem.

[lynnj]

Its not the Pythagorean Theorem.

[Jerch]

By the triangular inequality, we should know that the grooming parlour is inside the triangle of the other 3 shops (proof by contradiction). Alternatively, you could just look at the bazaar map.


Then what we have is actually one large triangle, and 3 smaller triangles that make up the large one.

Either by using:

A) Cosine Law +(angles at a point = 360 deg)
B) Heron's formula + (area of small triagles=area of large one)
C) Combination of those two

etc. we could obtain the answer. Out of those three, A's pretty simple with a graphical calculator... just use arc cosine...

[lynnj]

I used the Cosine Law!

[Shadow_Twisted]

If you ask me, it doesn't seem really necessary to go to those extremes. They gave you enough distances that make it appear all too easy to just use a very simple method.

Assuming the distance between the Grooming Parlour and the Smoothie Store is less than the distance between the Petpet Supplies shop and the Smoothie Store, what is the distance between the Grooming Parlour and the Smoothie Store?

I took that to mean using the triangle with the Grooming Parlour, Smoothie Store, and Petpet Supplies, that the distance between the Petpet Supplies and Grooming Palour is the hypotenuse(sp?). I can understand using a different method, but if we both arrive at the same answer, I don't see why people would want to use the more complex method.

If I'm wrong and you had a different answer than the one my method yields, please tell me. (Via a PM, no need to clutter this with too many arguments) I just feel that the Cosine Law is a bit too... complex. Then again, LCs have been known to use some complex math.

[Jerch]

If you ask me, it doesn't seem really necessary to go to those extremes. They gave you enough distances that make it appear all too easy to just use a very simple method.

Assuming the distance between the Grooming Parlour and the Smoothie Store is less than the distance between the Petpet Supplies shop and the Smoothie Store, what is the distance between the Grooming Parlour and the Smoothie Store?

I took that to mean using the triangle with the Grooming Parlour, Smoothie Store, and Petpet Supplies, that the distance between the Petpet Supplies and Grooming Palour is the hypotenuse(sp?). I can understand using a different method, but if we both arrive at the same answer, I don't see why people would want to use the more complex method.

If I'm wrong and you had a different answer than the one my method yields, please tell me. (Via a PM, no need to clutter this with too many arguments) I just feel that the Cosine Law is a bit too... complex. Then again, LCs have been known to use some complex math.

All I did was took a look at the problem and stuck all the variables into the calculator using the method that seemed most straight forward (cosine law) (I was a bit too lazy to find right angles)... whatever works...[though I still don't get what you're saying...]