I would suggest individually - there's no neat way to connect the circle otherwise
completely fence all three-i believe they mean it's altogether
Br0ken_xoxo wrote:Gilbert the Gelert farmer (He's a Gelert who happens to be a farmer, not a farmer who grows Gelerts!) has three fields. One field is an equilateral triangle, one field is a circle, and one field is a square. The square field is 75% larger in area than the triangular field, and 50% larger in area than the circular field. In order to completely fence all three of the fields, exactly 4000 metres of fencing is required.
when they say that do they mean individualy or alltogether as if they were connected?
Well, he has THREE fields, so I'm assuming they're not connected. If they were, it would be one field...
so my theory is:
divide that 4000 into sections based on the percentages they give you (square (50%)>circle and square (75%)> triangle) and figure out the sides and or diameter and take it from there..
Quote:Well, he has THREE fields, so I'm assuming they're not connected. If they were, it would be one field...
But it would still be a total of 4000 even if they aren't connected
Triangle is a bit tricker
A = 1/2 L1 * L2
in the case of an equilatoral triangle, all 3 angles are 60 degrees.
So the Sine of 60 degrees = Opposite / Hypotenuse
We need to figure out the Length of a side.
If we bisect an equilatoral triangle, the hypotenuse of the new one is L units long, and the short side is L/2
unfortunately, we need to figure out the long side.
Using the Sine formula:
Sine (60 degrees) = Opposite / L
So Opposite = Sine(60) / L
our equalatoral triangle's area = twice of our divided triangle. (Or actually, the same area as a rectangle of length L by Opposite)
so area = L * opposite
or area = L * L * sine(60)
solving for L:
L = sqrt(area/sin(60))
Right?
(and this is why I double check my formulas - my earlier one was wrong)
you could use trig but you still need atleast one side tho = /
marty22sam wrote:(and this is why I double check my formulas - my earlier one was wrong)
Aww...poop. I already entered that, assuming you were right. YOU LET ME DOWN!
Double the theoretical area of the triangle, then calculate the length of the sides by treating it as a square
I think that'd work
well nvm.. theresd a reverse trig thing that i cant remember the formula for.. now i regret throwing that book out.. >.<
Okay, using the corrected forumal, if you plug in a Square Area of 378057.5
the total fence length is 4000
and total area is 846128.6905
So the answer would be 846129 square meters?
Quote:So the answer would be 846129 square meters?
That's a pretty big number, you sure it's right?
That needs some more thinking though!
According to the spreadsheet, a circle is only 42 meters around, and the square/triangle are 1400 and 2400???
I know a circle is more efficient, but that seems wrong too!
that doesnt sound right to me.. = /
Perimeter
circle + triangle + square = 4000
where
square is 75% larger than triangle and 50% larger than circle.
gives formula:
b + a + 4a = 4000
where b = 4a/2
Solve a,b
a = 4000/7 and b = 8000/7
a = 571.42857
b = 1142.85714
thus perimeters are
triangle = 571.42857
circle = 1142.85714
square = 2285.71429
Knowing that circumference of circle is Pi*d
we can find area of circle Pi*r squared:
1142.85714/Pi = 363.63636 = d
d/2 = r
Pi*r squared = 103896.101789 sq m
From original statement we know
area of square is 50% larger than circle
so area of square = area of circle *1.5
= 155844.15268 sq m
also area of square is 75% larger than triangle
so
area of triangle = area of square/1.75
= 89053.80153 sq m
Total area =348794.055999
rounded to nearest whole number:
348794
Disregard - I had an extra SQRT in my circle formula.
Correct formula for circumference should be: 2*PI()*SQRT(B5/PI())
Okay. that seems better.
Total square area: 183753.5
total area of all: 411257.8333
411258 - sound better?
oops NVM. I'm not sure what to choose. :/
i duno = / if dif answers keep comming up whos saying that this one isnt wrong either.. (no offence)
