SOLUTION: A 2x3 foot cage is just right for 12 rabbits. By what factor do the dimensions need to be multiplied to get a cage just right for 3 times as many rabbits? What about for 108 rabbi

Question 1157624: A 2x3 foot cage is just right for 12 rabbits. By what factor do the dimensions need to be multiplied to get a cage just right for 3 times as many rabbits? What about for 108 rabbits?

Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A 2x3 foot cage is just right for 12 rabbits.
By what factor do the dimensions need to be multiplied to get a cage just right for 3 times as many rabbits?
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You can make it 6 by 3, or 2 by 9 feet.
2*3 = 6 sq feet.
Any pair of factors that have a product of 18, tho making narrower than 2 feet might stress the rabbits.
If you want it similar (2 dim's multiplied by the same factor), multiply each by .
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What about for 108 rabbits?
9 times the area.
2 by 3 ---> 6 by 9 to be similar.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
2 by 3 cage is just right for 12 rabbits.
a 2 by 3 cage has 2 * 3 = 6 square feet.
that implies 6/12 = .5 square feet per rabbit.

if you have 36 rabbits, then you would need 36 * .5 = 18 square feet of cage.
if you let x equal the factor that you need to multiply the original dimensions by to get 18 square feet, then the equation is:
3x * 2x = 18
this becomes 6x^2 = 18
solve for x to get x = sqrt(18/6) = sqrt(3).

for 108 rabbits, the new amount of square feet needs to be 108 * .5 = 54 square feet.
if you let x equal the factor that you need to multiply he original dimensions by to get 54 square feet, then the equation is:
3x * 2x = 54.
this becomes 6x^2 = 54
solve for x to get x = sqrt(54/6) = sqrt(9) = 3

your solution is:
for 36 rabbits, the factor is sqrt(3).
for 108 rabbits, the factor is 3.

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