Depth - Pond

[Guest]

A square pond is 12 units on a side. In the middle of the pond is a reed that is 1 unit above the water. The reed is pulled to the middle point of one of the edges and just touches the top of the water.

Determine depth of water in the center.

[Guest]

length of reed is d + 1
depth = d
dist to middle of pond = 6

(d + 1)^2 - d^2 = 6^2
d^2 + 2d +1 - d^2 = 36
2d +1 = 36
2d = 35
d = 17.5

...................Simple.......................

[Guest]

"(d + 1)^2 - d^2 = 6^2"

I am not clear on this step.

[Guest]

Pythagoras theorem
Right angle triangle 3 sides as below
6 units from centre of pond to middle of edge
the reed is (d+1) units long
depth is d units

[Guest]

"Pythagoras theorem"

A^2 = B^2 + C^2

I still don't understand.

[Guest]

OK, in your terminology

A = (d+1) the sloping side
B = d the vertical side
C = 6 the horizontal side

(d+1)^2 = d^2 + 6^2

or re-arranged, bring the "d"s all over to LHS

(d+1)^2 - d^2 = 6^2

[Guest]

Ok, but I am not clear.