Find the length, in feet, of the ladder.

Question

A ladder of length 2x+1 feet is positioned against a wall such that the bottom is x−1 feet away from a wall. The distance between the floor and the top of the ladder is 2x feet.

Answer 1

If you draw a diagram you will see that the ladder, the wall and the floor form a right triangle.  The hypotenuse of the triangle is the ladder, the wall and the floor are the legs.  So by the Pythagorean Theorem 

 

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

4x^2 + 4x + 1 = x^2 - 2x + 1 + 4x^2

0 = x^2 -6x

x(x-6) = 0

 

x = 0 or x = 6

 

Discard x = 0 since it will give a negative distance for how far away the bottom of the ladder is from the wall 

 

So the ladder is 2*6 + 1 = 13 feet long

 

Check:  Ladder = 13

           Wall height to top of ladder = 12 

           Bottom of ladder to wall = 5 

           A 5 - 12 - 13 right triangle