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

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0