2005 PMWC Problems/Problem I13
Problem
Sixty meters of rope is used to make three sides of a rectangular camping area with a long wall used as the other side. The length of each side of the rectangle is a natural number. What is the largest area that can be enclosed by the rope and the wall?
Solution
Let be the side parallel to the wall, and adjacent to the wall. Then . The area of the rectangle is ; this is a quadratic equation, which we can maximize using the formula . Hence the area is .
See also
2005 PMWC (Problems) | ||
Preceded by Problem I12 |
Followed by Problem I14 | |
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 |