How deep is the water?

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 notes that the freshly cut stem now just barely crests the top of the water.

How deep is the pond?

Originally posted by PBE6
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?

4 feet

Originally posted by uzless
4 feet

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 PBE6
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.

It's a 5-12-13 triangle, so 12 ft.

but I've never seen a pond with flowers growing in it that has banks that steep 🙂

The flower itself has no height? Just the stem.

Originally posted by PBE6
A woman walks by a pond...
How deep is the pond?

Insufficient information.

Originally posted by forkedknight
It's a 5-12-13 triangle, so 12 ft.

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?

Wrong, unless this is another trick question. One is only given that a flower with a 1 foot stem is growing out of the water, and is removed.

Originally posted by eldragonfly
Wrong, unless this is another trick question. One is only given that a flower with a 1 foot stem is growing out of the water, and is removed.

No, the stem reaches to the bottom of the pond. Only one foot extends above the water.

Originally posted by AThousandYoung
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?

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

Originally posted by AThousandYoung
No, the stem reaches to the bottom of the pond. Only one foot extends above the water.

insufficient information.

Originally posted by eldragonfly
insufficient information.

quit babbling and do some math.

Originally posted by forkedknight
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

Ok. I suppose I should have realized to use the Pythagorean. I mean, I was a TA in middle school math all last year.

Originally posted by eldragonfly
Insufficient information.

Now THAT would have been funny, but you wrecked it by being serious. 🙄