# math

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Lighting hit a tree three-eighths of the distance up the trunk from the ground and broke the tree so that its top landed 40 feet from the base of the trunk. How tall was the originally tree?

• math -

The wording is somewhat ambiguous. The way I read it says that the part that fell off must be 5/8 of the tree

so (5/8)x = 40
5x = 320
x = 64

or

Is the part that broke off still attached and when bent over lands 40 feet from the tree?

then (3x/8)^2 + 40^2 = (5x/8)2
9x^2/64 + 1600 = 25x^2/64
(16/64)x^2 = 1600
take √ of both sides
(1/2)x = 40
x = 80

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