May 2011
Problem of the Month

Pond Problem

A pond has a diameter of 10 feet.

At the center of the pond, a weed sticks up 1 foot out of the water.

When the weed is bent over, the top of it touches the bank at the water level.

How deep is the pond?

Solution to the Problem:

The pond is 12 feet deep.

Let x = depth of the pond.

Then x + 1 = length of the weed.

When the weed is bent over, it becomes the hypotenuse of a right triangle.

The radius of the pond is 5 feet.

So, x² + 5² = (x + 1)²

Then x² + 5² = x² + 2x + 1

So, 25 = 2x + 1

So, x = 12 feet (the depth of the pond) and x + 1 (the length of the weed) is 13 feet.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Josey Pitts	Mountain View High School, Mountain View, Wyoming
3. Sammy Hood	Mountain View High School, Mountain View, Wyoming
4. murrayb@kpmath.com	Mountain View High School, Mountain View, Wyoming
5. Jacob Harmon	Mountain View High School, Mountain View, Wyoming
6. Austin Hale	Mountain View High School, Mouuntain View, Wyoming
7. Crystal Schleichardt	Mountain View High School, Mountain View, Wyoming
8. Jessica Driapsa	Mountain View High School, Mountain View, Wyoming
9. Chad Fore	Scott County, Virginia
10. Bo Aimone	Mountain View High School, Mountain View, Wyoming
11. Kurtis Romero	Mountain View High School, Mountain View, Wyoming
12. Jordan Madsen	Mountain View High School, Mountain View, Wyoming
13. Alexis Condos	Mountain View High School, Mountain View, Wyoming
14. Earl Hickman	Mountain View High School, Mountain View, Wyoming
15. David & Judy Dixon	Bennettsville, South Carolina

Send any comments or questions to: David Pleacher