You have 1200 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. what are the largest dimensions of this enclosure that you could build?

step-by-step explanation: problem n' solution

you have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. what are the largest dimensions of this enclosure that you could build?

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make a drawing and denote:

x = half of the length of the enclosure

2x = the length of the enclosure

y = the width of the enclosure

p = 800 ft the perimeter

the perimeter of the two enclosures can be expressed p = 4x + 2y thus

4x + 3y = 800

solving for y:

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y = 800/3 - 4x/3

the area of the two enclosure is a = 2xy.

substituting y = 800/3 - 4x/3 in a = 2xy we get

a = 2x(800/3 - 4x/3)

a =1600x/3 - 8x^2/3

we need to find the x for which the parabolic function a = (- 8/3)x^2 + (1600/3)x has maximum:  

x max = -b/2a, a = (-8/3), b = 1600/3

x max = (-1600/3)/(2*(-8/3))

x max = 100 ft

y = 800/3 - 4*100/3

y = 133.33 ft

2x = 2*100

2x = 200 ft

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expression #3 is not equivalent. the others are.

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles