The foot of a ladder is placed 10 feet from a wall. If the top of the ladder rests 13 feet up on the wall, find the length of the ladder.

Distance on ground = 10 feet

Length of ladder (hypotenuse) = x          [unknown for now]

Height on wall =  x-2

The Pythagorean theorem says, for a right triangle:    a2+b2=c2

    [note: the hypotenuse, c, is always the longest side]

   102  + (x-2)2  =   x2

  100 + x2 -4x + 4 =  x2       [expand using F-O-I-L]

   100 -4x + 4 = 0                [subtract x2 from both sides]

  104 - 4x = 0                    [collect terms]

    -4x = -104               [subtract 104 from both sides]

     x = 26             [divide both sides by (-4)]

Check:

  Is   102 + 242 = 262   ?

        100 + 576 = 676   ?

         676 = 676   ?yes

-4

step-by-step explanation: