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The top of a pole rests 8 feet above the ground along a wall. If the bottom of the pole is moved another 2 feet from the wall, the entire pole will lie on the ground with the top of the pole touching the wall. In feet, how long is the pole?

 Jul 13, 2020
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Originally, there is a right triangle:  call the length of the pole "p"

At first, the distance from the bottom of the pole to the wall is "g"

and the distance from the top of the pole to the ground is 8.

--->   p2  =  g2 + 82

 

If the pole is moved another 2 feet from the wall, it will lie on the ground; now the distance from the bottom of the 

pole to the wall is  g + 2; so  p  =  g + 2.

 

Substituting  "g + 2" for "p" in the above equation:  (g + 2)2  =  g2 + 82 

                                                                           g2 + 4g + 4  =  g2 + 64

                                                                                   4g + 4  =  64

                                                                                         4g  =  60

                                                                                           g  =  15

 

The pole is  g + 2  =  17

 Jul 13, 2020

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