This famous puzzle is about a water lily that Henry W. Longfellow introduced into his novel, Kavenaugh:?

This famous puzzle is about a water lily that Henry W. Longfellow introduced into his novel, Kavenaugh:


When the stem of a water lily is vertical the blossom is 10 centimeters above the surface of the lake. If you pull the lily to one side keeping the stem straight the blossom touches the water at a spot 21 centimeters from where the stem formerly cut the surface. How deep is the water?

This famous puzzle is about a water lily that Henry W. Longfellow introduced into his novel, Kavenaugh:?
Depth of water = x


Height of water lily = (x+10)





x, 21 and (x+10) form a right-angled triangle, with (x+10) as the hypotenuse.





x² + 21² = (x+10)²


x² + 441 = x² + 20x + 100


20x = 341cm


x = 17.05cm





The depth of the water is 17.05cm.
Reply:Let d = depth of water


=%26gt; (d + 10)^2 - d^2 = (21)^2


=%26gt; 10 * (2d + 10) = (21)^2


=%26gt; d


= (44.1 -10) / 2


= 17.05 cm.
Reply:21^2 = 10*depth.





depth = 44.1 cm.
Reply:For 2 intersecting chords A and B of a circle, the product of the divided lengths of Chord A and Chord B are equal.





The stem of the lily is attached at the center of the circular arc of radius R you get by pulling the lily to the side, and at the lake bottom. (Draw the picture!)





So 10*(d+R)=21*21, and R=10+d


10*(2d+10) = 441


20d = 341


d = 17.05 cm