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

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) (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

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
RELATED QUESTIONS
A ladder is resting against a wall. The top of the ladder touches the wall at a height of (answered by rfer)

A ladder is resting against a wall. The top of the ladder touches the wall at a height of (answered by user_dude2008)

A ladder is resting against a wall. The top of the ladder touches the wall at a height of (answered by richwmiller)

A ladder is resting against a wall. The top of the ladder touches the wall at a height of (answered by fractalier)

a ladder is resting against a wall. the top of the ladder touches the wall at height of... (answered by mananth)

A ladder is resting against a wall. The top of the ladder touches the wall at a height of (answered by mananth)

A ladder is resting against a wall. The top of the ladder touches the wall at a height... (answered by Greenfinch)

a ladder is resting against the wall. the top of the ladder touches the wall at a height... (answered by checkley77,jojo14344)

a ladder is resting against a wall. The top of the ladder touches the wall at a height of (answered by rfer,solver91311)