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:
Answer Choices:
A.
B.
C.
D.
E. infinitely many
Solution:
From the given conditions we have (1) and (2) . Divide equation (2) by equation (1): . This is impossible since both and are less than and less than .