Originally posted by PBE64 feet
A woman walks by a pond, and sees a beautiful flower growing on a stem in the middle of the pond. She finds a 5 foot stick by the pond, which just allows her to reach the flower and drag to the edge, where the flower just touches the water. She then picks the flower with 1 foot of the stem attached, and lets the rest float back to the centre of the pond. She ...[text shortened]... that the freshly cut stem now just barely crests the top of the water.
How deep is the pond?
Originally posted by uzlessNope, but I should clarify the wording in the problem.
Originally posted by PBE6It's a 5-12-13 triangle, so 12 ft.
Nope, but I should clarify the wording in the problem.
The distance from the edge of the pond to the flower is 5 feet, and the flower sticks out 1 foot above the surface of the water before being cut. You can assume that the flower stem is taught and remains a straight line from the flower to the centre-bottom of the pond at all times.
Originally posted by AThousandYoung5^2 + D^2 = (D+1)^2
That's one possibility, but are there any others?
It's clear that it's a 5-D-(D+1) right triangle, but is 5-12-13 the only one of those?
Originally posted by forkedknightOk. I suppose I should have realized to use the Pythagorean. I mean, I was a TA in middle school math all last year.
5^2 + D^2 = (D+1)^2
25 + D^2 = D^2 + 2D + 1
2D = 24
D = 12
It's the only right triangle where the short side is 5 and the other sides have a difference of 1