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.
What is the total area of all three fields, in square metres?
First question is what do they mean by 50% larger.
If field A is 100 sq meters, does that make Field B 75 square meters?
Or 50 square meters?
Means it's 150% the size of the other field
So to make it simple:
Area of Triangle = Area of Square / 1.75
Area of Circle = Area of Square /1.5
Correct?
I think that's right, I worked it all out into fractions of x
I used a spreadsheet to figure it out.
Assuming that:
ACircle = ASquare/1.5
ATriangle = ASquare/1.75
then
totalArea = ASquare + ASquare/1.5 + ASquare/1.75
(continued shortly)
Changing to fractions:
total area = S + 4/7 S + 2/3 S
Simplifying:
total area = 21/21 S + 12/21 S + 14/21 S
total area = 47/21 S
So area of square (S) = 21/47 total area
Not sure where I'm going with this... so I'll explain the spreadsheet instead
I think you're heading in the right direction there
...nevermind, just kidding
EDIT: I'm stupid.
Down the left side, labeled Square, Circle, Triangle, Total
Next column = areas.
Square = (plug in some number)
Circle = (square/1.5)
Triangle = (square/1.75)
Next column over is formula for a "side"
Square = Sqrt(area of square)
Circle = 2 * pi * sqrt(area of quare / Pi)
Triangle = Sqrt((2 * area of square) / sin(degrees(60))
Next column is total length of sides
Square = 4 * square side
Triangle = 3 * triangle side
circle = circle side. (circumference)
Under that is total length = sum (square + circle + triangle)
Now you just tweak initial area of square...
equation
why would it be 1.75 and 1.50 wouldnt it just me .75 and .50 becuase when u convert a percent to a decimal u move the % to the left twice.. no one infront of it = /
Assuming all those formulas are right, If you plug in a Square area of 282929.2
the total fence comes out to 4000
and total area comes to 633222.4952
But that's subject to review of the formulas of course...
Re: equation
Br0ken_xoxo wrote:why would it be 1.75 and 1.50 wouldnt it just me .75 and .50 becuase when u convert a percent to a decimal u move the % to the left twice.. no one infront of it = /
Yeah....but if it's 50 percent bigger, that means that it's 100% of the size, plus that 50%, making it 1.5 times that size.
Side of a square = sqrt(area)
Pretty sure that is correct.
Side of circle. (Circumference)
C = 2 Pi R
and Area = Pi R * R
solving for r: R = sqrt(Area/Pi)
plug into circumference formula:
C = 2 * pi * sqrt(area/Pi)
Sound good?
try 2345 for tha area of the square
Wow, missed a whole page here
NM!
area formulas:
square= side squared
circle= (pi)radius squared
triangle= (base)(height)/2
lc
I have no clue with this one cause math is my weakest subject... now letter I am fine with..... So would you mind helping me out too? Thank you
math is my favorite subject how ever i've been out of school for a few months now so i'ma bit rusty XD
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?
