OK can some please answer this riddle?

Question

A farmer 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.

People, it's SUMMER. This isn't math homework.

Oh sorry, the question is What is the area?

Answer 1

So what is the question?(if the total area you seek for then Area (total)= (456)^2 (1+ .25 +.5)= 363,888 ft squared

I assume you want to find out how much of field area the farmer has.

Perimeter=
=P(square)+P(triangle)+P(circle)=
=4a+3t + 2 Pi r

Also we know that
A(circle)=Pi r^2
A(triangle)=.866 t ^2 [A=.5 t (t sin(60))=. 433 t ^2 ]
A(square)=a^2
(1/4)A(square)=A(triangle) since the square is 75% larger
(1/2)A(square)=A(circle)

So we have
(1/4) a^2=.433 t ^2
t = ( .76 ) a

Similarly
(1/2)a^2= pi r^2
r =.4a

Now
P(total) =4a+3t + 2 Pi r=4000
Or
P( total) = 4a + 3( .76 ) a + 2 Pi (.4a)=
P( total) = 4a + 2.28 a + 2.5a = 8.78 a

a = 4000/=456 feet
t = 346 and
r = 195

Okay then the area is

Area (total)= (456)^2 (1+ .25 +.5)= 363,888 ft squared

Answer 2

This question has been around a while, and maybe Edward D has already answered it, but I'll give it a crack. T, C, and S will mean triangle, circle, and square.

S = 1.75T = 1.5C
T = (4/7)S; C = (2/3)S

T = bh/2 = (b/2)[b sqrt(3)/2] = (b^2) sqrt(3)/4
base b = 2 sqrt[T/sqrt(3)]

C = pi r^2 ==> r = sqrt(C/pi)
Circumference c = 2 pi r = 2 sqrt(pi C)

4 sqrt S + 6 sqrt[T/sqrt(3)] + 2 sqrt(pi C) = 4000
4 sqrt S + 6 sqrt[4S/(7 sqrt(3))] + 2 sqrt(2 pi S/3) = 4000
{4 + 12 / sqrt[7 sqrt(3)] + 2 sqrt(2 pi/3)} sqrt S = 4000
10.34 sqrt S = 4000
S = 149,630.6 sq m.
T = (4/7)S = 85,503.2 sq m.
C = (2/3)S = 99,753.7 sq m.

Total area = S(1 + 4/7 + 2/3) = S(21+12+14)/21 = (47/21)S = 334,887.57 sq m.

Check: Perimeter of square = 1547.3 m
Perimeter of triangle = 1333.1 m.
Circumference of circle = 1119.6 m.

Total fencing = 4000 m

I can't see Edward's answer now, so I don't know if I got the same answer as him.

Answer 3

So basically what they're saying is:

1 square field equals 1 3/4 triangle fields.
1 square field equals 1 1/2 circle fields.

If square field is x...

4000 meters (metres)= 1x + 1.75x + 1.5x
= 4.25x
x= 4000/4.25
x= roughly 941

so the square field needs 941 meters
the triangle 941 times 1.75
the circle 941 times 1.5

Answer 4

Off the top ao my head, the square one is almost 2000, the triangluar one half of that and so forth....

Answer 5

And the name of the fence supplier is?

Answer 6

that's not a riddle. that's your math homework. turn off the computer, turn on your calculator and start figuring it out.

Answer 7

too much work... go outside and enjoy the summer day!

Answer 8

There is no question.

Answer 9

and what is the question??