Question

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?

Answer 1

Solution:-

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.

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

for 108 rabbits, the factor is 3. Answer