SOLUTION: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet. Find the distance from the wall to the bottom of the ladder if the length of the

Algebra ->  Pythagorean-theorem -> SOLUTION: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet. Find the distance from the wall to the bottom of the ladder if the length of the       Log On


   

Question 539689: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet. Find the distance from the wall to the bottom of the ladder if the length of the ladder is one foot more than twice its distance from the wall.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
height at which the ladder touches the wall = 15 ft

Distance from foot of the ladder to the wall= x

Length of the ladder = 2 x + 1

The ladder,the floor & the wall form a right triangle.
The base is one leg .The height is the other leg
The ladder acts as the hypotenuse
Pythagoras theorem

(Hyp)^2= (leg1)^2+ Leg2^2
(2x+1)^2 = X^2 + 15 ^2
X^2+4x + 1 =X^2+225

4X^2- x^2 + 4 x+ 1 -225

3 X^2- + 4 x -224

Find the roots of the equation by quadratic formula

a= 3 ,b= 4 ,c= -224

b^2-4ac= 16 + 2688
b^2-4ac= 2704
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%2B21%29%2F%2812%29
x1=( -4 + 52 )/ 6
x1= 8 ft
x2=( -4 -52 ) / 6
x2= -9.33
Ignore negative value
height at which the ladder touches the wall = 8 ft

m.ananth@hotmail.ca