3 March, 01:45

# Antonio is a biologist studying life in a pond. He needs to know how deep the water is. He notices a water lily sticking straight up from the water, whose blossom is 8 cm above the water's surface. Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot 40 cm from where the stem first broke the water's surface. How is Antonio able to calculate the depth of the water? What is the depth?

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1. 3 March, 02:16
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For this problem we can represent the situation as a rectangle triangle.

x: depth of water.

40: Base. "Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot"

x + 8: Hypotenuse. "He notices water lily sticking straight up from the water, whose blossom is 8 cm above the water's surface." Antonio pulls the lily to one side, keeping the stem straight, until the blossom touches the water at a spot".

By the Pythagorean theorem we have:

x ^ 2 + 40 ^ 2 = (x + 8) ^ 2

Clearing x:

x ^ 2 + 1600 = x ^ 2 + 16x + 64

x ^ 2 - x ^ 2 = 16x + 64 - 1600

0 = 16x - 1536

1536 = 16x

1536/16 = x

x = 96