1963 AHSME Problems/Problem 32
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.