Quandaries and Queries


Hello! My question is each side of a square S is 18 inches long and the area of S is at least 3 times the area of a rectangle that is 9 inches wide. What is the greatest possible length in inches of the rectangle?

Other.  I am just curious. i would say maybe a 6th grade question.

thank you for your help




Hi Rebecca,

Since the square has each side of length 18 inches its area is 182 = 324 square inches. Since the area of the square is at least three times the area is the rectangle, the largest area the rectangle can have is 3  324 = 972 square inches.

The rectangle is 9 inches wide so its area is 9 its length. Thus

9 length is at most 927

Hence the length is at most 927/9 = 103 inches.



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