AMC10 2009 B

AMC10 2009 B · Q10

AMC10 2009 B · Q10. It mainly tests Pythagorean theorem, Coordinate geometry.

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 $x$?

一根旗杆原来高 5 米。飓风从离地面 $x$ 米处将其折断，上部仍附着在残桩上，触地时距基部 1 米远。$x$ 是多少？

(A) 2.0 2.0

(B) 2.1 2.1

(D) 2.3 2.3

(E) 2.4 2.4

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): Let $x$ be the height of the stump. Then $5-x$ is the height of the snapped part, now forming the hypotenuse of a right triangle. By the Pythagorean Theorem, $$ x^2+1^2=(5-x)^2=x^2-10x+25 $$ from which $x=2.4$.

答案（E）：设 $x$ 为树桩的高度，则 $5-x$ 为折断部分的长度，它现在构成一个直角三角形的斜边。由勾股定理， $$ x^2+1^2=(5-x)^2=x^2-10x+25 $$ 由此得 $x=2.4$。

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