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 |