SOLUTION: In a pond there is a flower with a stiff rooted at the bottom of the pond. The flower stands straight up and extends 5 cm above the surface of the water. When the top of the flower

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Question 1027826: In a pond there is a flower with a stiff rooted at the bottom of the pond. The flower stands straight up and extends 5 cm above the surface of the water. When the top of the flower is shifted 20 cm to one side, the flower sinks below the surface of the water. How deep is the pond?
Answer by ikleyn(52794) About Me  (Show Source):
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In a pond there is a flower with a stiff rooted at the bottom of the pond. The flower stands straight up and extends 5 cm above
the surface of the water. When the top of the flower is shifted 20 cm to one side, the flower sinks below the surface of the water.
How deep is the pond?
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Let "x" be the depth of the pond, in centimeters.

Then the height of the flower in its vertical position is (x+5).

When the top of the flower is shifted in 20 cm, we get the right angled triangle with one leg of "x" cm, the other leg 20 cm and the hypotenuse of (x+5) cm.

So, you have an equation

x%5E2+%2B+20%5E2 = %28x%2B5%29%5E2.

Simplify and solve it:

x%5E2+%2B+400 = x%5E2+%2B+10x+%2B+25,

10x = 375,

x = 375%2F10 = 37.5.

The depth of the pond is 37.5 cm.
The height of the flower is 37.5 + 5 = 42.5 cm.