SOLUTION: Hello, I am not quite sure how to approach this problem: when the lower end of a ladder that had been resting flat against a wall was pulled out 4 feet, the top of the ladder de

Algebra ->  Pythagorean-theorem -> SOLUTION: Hello, I am not quite sure how to approach this problem: when the lower end of a ladder that had been resting flat against a wall was pulled out 4 feet, the top of the ladder de      Log On


   

Question 31464: Hello, I am not quite sure how to approach this problem:
when the lower end of a ladder that had been resting flat against a wall was pulled out 4 feet, the top of the ladder descended one-fifth the length of the ladder. find the length of the ladder.
Thanks so much, really appreciate it.
Answer by blubunny01(20) About Me  (Show Source):
You can put this solution on YOUR website!
If you picture a ladder leaning against the wall, you can see that it forms a right triangle such that the ladder is the hypotenuse.
Let x = the length of the ladder (in ft).
We know that one side of the triangle is 4ft, and the other side of the triangle is 1/5 the length of the ladder, which is (1/5)x.
So, if we plug this knowledge into the pythagorean theorem, we have:
a = 4ft
b = x/5
c = x
%284%29%5E2+%2B+%28x%2F5%29%5E2+=+x%5E2

16+%2B+x%5E2%2F25+=+x%5E2

16+=+x%5E2+-+x%5E2%2F25

16+=+%2824%2F25%29x%5E2

16%2A%2825%2F24%29=+x%5E2

2%2A%2825%2F3%29=+x%5E2

50%2F3+=+x%5E2

sqrt%2850%2F3%29+=+x

5%2Asqrt%282%2F3%29+=+x

So, the length of the ladder is 5sqrt%282%2F3%29 ft, or approx 5.816 ft.