SOLUTION: Iva is trapped in a house which has walls 15 feet high. Fire fighters will rescue him by putting a ladder of length L feet at a distance x feet from the wall. They require x/L=1/2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Iva is trapped in a house which has walls 15 feet high. Fire fighters will rescue him by putting a ladder of length L feet at a distance x feet from the wall. They require x/L=1/2      Log On


   

Question 187015: Iva is trapped in a house which has walls 15 feet high. Fire fighters will rescue him by putting a ladder of length L feet at a distance x feet from the wall. They require x/L=1/2 solve exactly for x and L.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Our calculations will be based on the assumption that one end of the ladder will rest on the top of the 15ft wall. The rest wil look like this:
--->Condition:x%2FL=1%2F2=L=2x
That forms a Right Triangle, Pyth.Theorem remember?
L%5E2=15%5E2%2Bx%5E2---> as per condtn:L=2x
%282x%29%5E2=225%2Bx%5E2
4x%5E2=225%2Bx%5E2--->4x%5E2-x%5E2=225
3x%5E2=225---->cross%283%29x%5E2%2Fcross%283%29=cross%28225%2975%2Fcross%283%29
x=sqrt%2875%29=highlight%288.66ft%29, Distance from the Wall
Remember our condition:x%2FL=1%2F2
8.66%2FL=1%2F2--->L=8.66%2A2=highlight%2817.32ft%29,Length of Ladder
.
Let's check by going back to our Eqn:
17.32%5E2=15%5E2%2B8.66%5E2
300ft%5E2=225ft%5E2%2B74.9956ft%5E2
300ft%5E2=300ft%5E2, close enough, we round off.
Thank you,
Jojo