i need help

Question

A ladder is propped against the side of a building. If the bottom of the ladder is 7 feet away from the base of the building the height at which the top of the ladder touches the building is 1 foot less than the  length of the ladder, how high up the building is the top of the ladder?

Answer 1

First, draw a picture.  This is a right triangle with:

   7 foot base

   x for height      [one foot less than (x+1)]

   (x+1) for hypotenuse (the length of the ladder)

 

From the Pythagorean Theorem:

    7² + x² = (x+1)²

    49 + x² = x² + 2x + 1          [use F-O-I-L to expand expression]

    49 = 2x + 1                  [subtract x² from both sides]

    48 = 2x                [subtract 1 from both sides]

     24 = x             [divide both sides by 2]

 

Let's check:

  Is  7² + 24² = (24+1)²   ?

      49 + 576 = 625   ?

        625 = 625   ?yes

Answer 2

7^2+ (x-1)^2 = x^2

x=25

x-1=24 is your answer