Problem: If the perimeter of rectangle is inches, the least value of diagonal , in inches, is:
Answer Choices:
A.
B.
C.
D.
E. none of these
Solution:
Let the dimensions be and and let the diagonal be . Then . The least value of (and, hence, of ) occurs when .
(least) .
or
The graph of is a parabola with the low point (minimum) at vertex . (least) and d (least) .
or
Of all rectangles with a fixed perimeter the one with least diagonal is the square. Since the perimeter is 20 , the side of the square is 5 , and, therefore, d=\sqrt