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Regions I, II and III are bounded by squares. The perimeter of region I is 12 units and the perimeter of region II is 24 units. What is the ratio of the area of region I to the area of region III? Express your answer as a common fraction.
 

 
Lightning  Oct 11, 2018
 #1
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The mathy way of doing this is noting that for a square the perimeter is a function of s while the area is a function of s

 

So an increase in the perimeter by a factor of K leads to an increase in area by a factor of K2

 

or in even more mathy terms, the area is directly proportional to the square of the perimeter

 

Another way of putting this is

 

\(\dfrac{A_1}{A_2} = \left(\dfrac{P_1}{P_2}\right)^2 \\ \dfrac{A_1}{A_2} = \left(\dfrac{12}{24}\right)^2 = \dfrac 1 4\)

 
Rom  Oct 11, 2018

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