2009 AMC 10B Problem 10

Question

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?

2.0

2.1

2.2

2.3

2.4

The broken piece has length

5-x

and forms the hypotenuse

x^2+1^2=(5-x)^2

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}

so

10x=24

and

x=2.4.

Thus, the correct answer is E.

Problem 10 in other years