# Math Help - pole leaning on a wall- find length

1. ## pole leaning on a wall- find length

The height of a wall is 10m. a pole of unknown length leans against the wall so that the top is even with the top of the wall. If the bottom of the pole is moved 1m further from the wall, the pole will fall to the ground. What is the lenght of the pole?

2. You have a right triangle with vertical side 10, horizontal side x, and hypotenuse x+1. Use Pythagoras to solve for x.

3. Hello, nikie1o2!

The height of a wall is 10m.
A pole of unknown length leans against the wall
so that the top is even with the top of the wall.

If the bottom of the pole is moved 1 m further from the wall,
the pole will fall to the ground.

What is the length of the pole?
Code:
    A o
| *
|   *
|     *    ______
10 |       * √x²+100
|         *
|           *
|             *
C o - - - - - - o B
x

The pole is $AB.$
The wall is: . $AC = 10\text{ m}$
The bottom of the pole is $BC = x$ m from the wall.
The pole is: . $AB \:=\:\sqrt{x^2+100}$

If the bottom of the pole is moved 1 m further from the wall,
. . the pole will fall to the ground.

Code:
      |
|
|      ______
| - - √x²+100 - - :
A o * * * * * * o * o C
: - -  x  - - : 1 :

We have: . $x + 1 \;=\;\sqrt{x^2+100}$

Square: . $x^2 + 2x + 1 \;=\;x^2+100 \quad\Rightarrow\quad 2x \:=\:99 \quad\Rightarrow\quad x \:=\:\frac{99}{2}$

Therefore, the length of the pole is: . $x + 1 \;=\;\frac{99}{2} + 1 \;=\;\frac{101}{2}\;=\;50\tfrac{1}{2}\text{ m}$