SOLUTION: A 25-foot ladder is placed so that it reaches to a point on the wall that is 3 feet higher than 3 times the distance from the base of the wall to the base of the ladder How far fr

Algebra ->  Pythagorean-theorem -> SOLUTION: A 25-foot ladder is placed so that it reaches to a point on the wall that is 3 feet higher than 3 times the distance from the base of the wall to the base of the ladder How far fr      Log On


   

Question 468239: A 25-foot ladder is placed so that it reaches to a point on the wall that is 3 feet higher than 3 times the distance from the base of the wall to the base of the ladder
How far from the wall is the base of the ladder
How high does the ladder reach
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
the distance from the base of the wall to the base of the ladder =x
wall touching height = 3x+3
Ladder =25 feet
x%5E2%2B%283x%2B3%29%5E2=25%5E2
x%5E2%2B9x%5E2%2B18x%2B9=625
10x%5E2%2B18x-616=0
Find the roots of the equation by quadratic formula

a= 10 ,b= 18 ,c= -616

b^2-4ac= 324 + 24640
b^2-4ac= 24964
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2Bsqrt%2824%29%29%2F%2812%29
x1=( -18 + 158 )/ 20
x1= 7
x2=( -18 -158 ) / 20
x2= -8.8
Ignore negative value
7 feet from wall
3x+3 =24 feet ladder touching the wall