How deep is the water? Problem Solving?

Question

The poet Henry Wadsworth Longfellow, in his novel Kavenaugh, presented the following puzzle:

When a waterlily stem is vertical, the blossom is 10 cm above the water. If the blossom is pulled to the right keeping the stem straight, the blossom touches the water 21 cm from where the stem came through the water when vertical. How deep is the water?

Any help is appreciated!!

Answer 1

X = height of water

(X+10) = total length of stem

A^2 + B^2 = C^2

21^2 + X^2 = (10+X)^2

Solve for X.

Answer 2

depth of water = d

length of stem = d + 10

Pythagoras:

d^2 + 21^2 = (d+10)^2

d^2 + 441 = d^2 + 20d +100

d = 17.05cm

Answer 3

Always draw a picture of the problem if you can.

Here you have the vertical stem and the horizontal water surface forming a right angle. When the stem is pushed over, it will form the hypotenuse of a right triangle.

The stem depth is "D" cm and is one leg of the triangle. The other leg  is the 21 cm across the water. The hypotenuse is D + 10 cm

Do the pythogerian math

(D+10)^2 = D^2 + 21^2

I got a little bit over 17cm for the depth.

Just as Lunchtime and I did, it is helpful to use representative letters for the unknowns rather than "X" . It helps to keep things more easily identified and it avoids confusion between "X" as an unknown and "X as a function. In this case we both used "d " or "D" for depth.