SOLUTION: To reach a damsell in distress, a knight places a 13-foot ladder against the castle wall. The base of the ladder is 7 feet less than the distance from the top of the ladder to the

Algebra ->  Triangles -> SOLUTION: To reach a damsell in distress, a knight places a 13-foot ladder against the castle wall. The base of the ladder is 7 feet less than the distance from the top of the ladder to the       Log On


   

Question 1420: To reach a damsell in distress, a knight places a 13-foot ladder against the castle wall. The base of the ladder is 7 feet less than the distance from the top of the ladder to the ground. How high on the castle will the ladder reach?
Answer by usyim88hk(158) About Me  (Show Source):
You can put this solution on YOUR website!
So this will form a triangle:
(If you are in high level math, you will notice that it is a 5-12-13 triangle which has sides length of 5, 12 and 13, but if you don't, we will solve it now)
let x be the distance from the ladder to the ground
x^2 + (x-7)^2 = 13^2
x^2 + x^2 - 14x +49 = 169
2x^2 - 14x - 120 = 0
Now use the quardratic formula to solve:
x=%2814%2B-sqrt%28%28-14%29%5E2-4%282%29%28-120%29%29%29%2F%282%282%29%29
x=%2814%2B-sqrt%281156%29%29%2F4
x=%2814%2B-34%29%2F4
x = 48/4 or -20/4
x = 12 or -5
Because length of anything can not be a negative number, so 12 is the answer.