Yet another word problem

Question

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 21 ft. Find the length of the ladder if the length is 9 ft more than its distance from the wall.

Answer 1

Looks like you guys are dealing with pythagorean theorem.

 

     |\

     | \ 

     |  \

21 |   \  x+9

     |    \

     |     \

     |____\

        x

 

So a² + b² = c² in this case, the ladder (x+9) is the hypotenuse, so we have that

 

x² + 21² = (x+9)²

 

The good news is that once you multiply out the (x+9) times itself, the x² on each side will cancel out so you should just be able to solve for x without doing too much work.

 

x² + 441 = x² + 18x + 81      subtract x² and 81 on both sides

 

360 = 18x

 

x = 20  (careful, this isn't the ladder, but the distance from the wall)

 

x+9 = 29 ft.