SOLUTION: A tree is supported by a wire anchored at the ground 8m from its base. The wire is 4m longer than the height that it reaches on the tree, find the length of the wire.

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Question 1170789: A tree is supported by a wire anchored at the ground 8m from its base. The wire is 4m longer than the height that it reaches on the tree, find the length of the wire.
Answer by ikleyn(52814) About Me  (Show Source):
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A tree is supported by a wire anchored at the ground 8m from its base.
The wire is 4m longer than the height that it reaches on the tree, find the length of the wire.
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In this problem, you have a right angled triangle with the hypotenuse x meters (now unknown)

and the legs of 8 meters and (x-4) meters.


Write Pythagorean equation

    x^2 = (x-4)^2 + 8^2.


Simplify and find x

    x^2 = x^2 - 8x + 16 + 64,

    8x = 80

     x = 80/8 = 10.


ANSWER.  The length of the wire is 10 meters.

Solved.