2009 AMC 10B Problem 10

Problem 10 of 25EasierGeometry

A flagpole is originally

5

meters tall. A hurricane snaps the flagpole at a point

x

meters above the ground so that the upper part, still attached to the stump, touches the ground

1

meter away from the base. What is

x?

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Solution

The standing stump has height

x,

and the snapped piece of length

5-x

is the hypotenuse of a right triangle with legs

x

and

1.

By the Pythagorean Theorem,

\begin{aligned} x^2+1^2 &= (5-x)^2 \\ &= x^2-10x+25, \end{aligned}

10x=24

and

x=2.4.

Thus, the correct answer is E.