Ladder word problem

Question

A 10 foot ladder lean against a wall. The height of the top of the ladder above the ground is twice the distance from the wall to the bottom of the ladder. How high is the top of the ladder?

Answer 1

If you draw this out you have a right triangle where the length of the hypotenuse is 10ft.  Let x = distance from wall to base of the ladder, then the height from ground to top of laddder is 2x

 

Using the pythagorean theorem where a² + b² = c² with c designating the hypotenuse we get:

 

x² + (2x)²=10²

x² + 4x² = 100

5x² = 100

x² = 20

x = sqrt(20)

x = 2(sqrt(5))

 

Height on wall is 2x so the top of the ladder is

4(sqrt(5)) ft high