area of circle
Use the distances given: a=330, b=240, c=270 (it doesn't matter which side you assign as a, b, and c).
Re: area of circle
Lykandhed wrote:If S is the triangle's area and its sides are a, b and c, then the radius of the incircle (also known as the inradius) is 2S/(a+b+c))
I used Heron's Formula: S = sqrt[ p*(p-a)*(p-b)*(p-c)]
where p = ½ (a + b + c) is the semiperimeter, or half of the triangle's perimeter to calculate the area of the triangle.
Finally, pi*r*r = Area of the largest incircle.
AGH. Damn. I forgot Heron's Formula. I can't believe I forgot that.
I have an excuse though - I had to take standardized tests this morning. Yeah. X_X
so, do you have an answer then? This geometry stuff is greek to me? I have been out of school for 30 years almost. I would appreciate any help. Thanks so much!! ~Tami
zylaxidia wrote:Correct me if I'm wrong, cuz I havent done geometry in forever.
We want the incircle of the triangle. The radius of the incircle would be:
r=(2a)/p a being area, p being perimeter
So first we need to find the area of the triangle, which I got to be 31946.8
through 1/2bh (a long arduous process, I assure you).
Then, 2(31946.8)/(330+270+240) = 76.06
Area of a circle = (pi)r^2
=18176.36
Anyone know if this is right?
That's exactly what I got. Then round
Yeah, I got that too. Then I rounded it up to 18200.
Yay! They actually posted the answers!
If you visit the Food Shop, you'll see that in the URL, there appears "obj_type=1". Also in the Food shop, you'll see that the first word is "Welcome". If you change the URL so that it says "obj_type=2", you'll see that the first word is "Kauvara". And so on... So if you change the URL so that it says "obj_type=40", you'll see that the first word is "Faerieland". So that's the answer!
I used Heron's formula, and everything, but I think I made a typo when calculating it all!
Oh well, next week.
^NPLC, Jen Aside was talking about last week's LC.
I did it differently....
If we're trying to make the circle fit inside the triangle, wouldn't the diameter have to be shorter than the shortest altitude in the triangle?
I solved for all 3 altitudes, found the shortest, divided by 2 to get the radius
then I did pi*r^2 to get the area
rounded, it was 11300.
I got what zylaxidia got
and bobolas, I'm pretty sure that the shortest altitude divided by 2 wouldn't be the radius since the incenter doesn't necessarily divide the altitudes in half. ...Someone correct me if I'm wrong...
So is it: 18200 or 11300????
I am 90% that its 18,200. Heron's formula hasn't failed me before but I dont really understand what bobolas was talking about.
yep lenny is 18200 and the mystry pic is neogreeting number 481
New LC
In pirate lore, there is an area of the sea known as the "Maraquan Circle." In the Maraquan Circle, it is rumoured that storms arrive out of nowhere, navigation equipment doesn't work correctly, and ships vanish without a trace.
The Maraquan Circle is between Mystery Island, Krawk Island, and Maraqua. It should be noted that Mystery Island and Krawk Island are 240 kilometres apart, Krawk Island and Maraqua are 330 kilometres apart, and Mystery Island and Maraqua are 270 kilometres apart. The Maraquan Circle, according to legend, is defined as the largest possible circle that fits entirely within the triangle formed by those three islands.
What is the area of the Maraquan Circle, in square kilometres? Please round to the nearest hundred, and please only submit a number! (For example, if the answer is 5176 square kilometres, only submit the number "5200".) Submitting any information other than a number may result in your submission being marked wrong!
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I'm thinking (as only a 10th grade math student) that you need to find the altitudes to each other side to find the greatest distance? Then take the shortest altitude and make that the diameter of the circle?
Pure speculation.
Re: New LC
Avocado wrote:I'm thinking....
Pure speculation.
Do you have some objection to the solutions provided in the previous couple of pages of this thread...?
Eliz.
It isn't speculation. the formula for the radius of the circle inscribed inside a scalene triangle is sqrt[(s-a)(s-b)(s-c)/s] where s is the semiperimeter.
Re: New LC
stapel wrote:Avocado wrote:I'm thinking....
Pure speculation.
Do you have some objection to the solutions provided in the previous couple of pages of this thread...?
Eliz.
Wow... I thought it was a new conundrum
Sorry about that -.-
oceantribe wrote:yep lenny is 18200 and the mystry pic is neogreeting number 481
woot... and neopets messed up and sent me neomail twice and paid me twice so i got 12k from it instead of just 6k. thx
