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 $\displaystyle AB.$
The wall is: .$\displaystyle AC = 10\text{ m}$
The bottom of the pole is $\displaystyle BC = x$ m from the wall.
The pole is: .$\displaystyle AB \:=\:\sqrt{x^2+100}$
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: .$\displaystyle x + 1 \;=\;\sqrt{x^2+100}$
Square: .$\displaystyle x^2 + 2x + 1 \;=\;x^2+100 \quad\Rightarrow\quad 2x \:=\:99 \quad\Rightarrow\quad x \:=\:\frac{99}{2}$
Therefore, the length of the pole is: .$\displaystyle x + 1 \;=\;\frac{99}{2} + 1 \;=\;\frac{101}{2}\;=\;50\tfrac{1}{2}\text{ m}$