Magic belt

The magic rectangular belt has the property that whenever its owner wants something, the length of the belt is reduced to 1/2 and the width to 1/3. After three such wishes, the belt had an area of 4 cm2. What was its original length if the original width was 9 cm?

Correct answer:

b =  96 cm

Step-by-step explanation:

a=9 cm S2=4 cm2  a2=a (1/3)3=9 (1/3)3=310.3333 cm b2=S2/a2=4/0.3333=12 cm  b=23 b2=23 12=96 cm   Verifying Solution:  S1=a b=9 96=864 cm2

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