1963 AHSME Problems/Problem 32
Revision as of 17:30, 28 July 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 32 (credit to vinayak-kumar))
Problem
The dimensions of a rectangle are and , . It is required to obtain a rectangle with dimensions and , , so that its perimeter is one-third that of , and its area is one-third that of . The number of such (different) rectangles is:
Solution
Using the perimeter and area formulas, Dividing the second equation by the last equation results in Since , . Since , . That means This is a contradiction, so there are rectangles that satisfy the conditions.
See Also
1963 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 31 |
Followed by Problem 33 | |
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