Length of ladder?

Question

A ladder is resting against a wall. The top of the ladder touches the wall at the height of 12ft. Find the length of the ladder if the length is 4ft longer than its distance from the wall.

Answer 1

First, draw a picture and label height of 11, base of b, and ladder length of (b+4).

 

Now, the Pythagorean Theorem (since this forms a right triangle)"

        b² + 12² = (b+4)²      (note: the ladder is the hypotenuse)

        b² + 144  = b² + 8b + 16       (use FOIL)

               144 = 8b + 16             (subtract b² from both sides)

                128 = 8b                 (subtract 16 from both sides)

                16 = b

 

So, the length of the ladder (b+4) is 20 feet.

 

Also note:  One of the "special triangles" that appears very often in math problems has sides of:

               3n,  4n,  5n     (here, n=4)      These numbers are called Pythagorean Tripples

Answer 2

 

 

Let b = distance from the wall

Thus b + 4 = length of ladder

Given, a = 12 the height where the latter touches the wall

 

So usiing a² + b² = c², we substiute the values above:

 

12² + b² = (b + 4)²

 

144 + b² = b² +8b + 16

 

Subtracting b² from both sides,

 

144 = 8b + 16

 

Subtracting 16 from both sides;

 

128 = 8b

 

Dividing both sides by 8;

 

b = 16 feet

 

b + 4 = 20 feet