SOLUTION: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the dista

Algebra ->  Triangles -> SOLUTION: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the dista      Log On


   

Question 141055: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.
I know that visualy the ladder is x, the base from the ladder to the wall is x-3 and from the base to the top of the ladder it is x-4, I just don't klnow how to plug this into an equasion adn solve. Thank you.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
use the Pythagorean theorem.
x%5E2+=+%28x-3%29%5E2+%2B+%28x-4%29%5E2
x%5E2+=+x%5E2+-6x+%2B+9+%2B+x%5E2+-8x+%2B+16
0+=+x%5E2+-14x+%2B+25
Now use the quadratic equation to solve for x.
x+=+%2814+%2B-+sqrt%28+14%5E2-4%2A1%2A25+%29%29%2F%282%29+
x+=+%2814+%2B-+sqrt%2896%29%29%2F%282%29+
You take in from here :)