Question 653283: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9 ft. Find the length of the ladder if the length is 3 ft more than its distance from the wall.
Answer by shweta(56)   (Show Source):
You can put this solution on YOUR website! Ladder is resting against a wall, so it is making a slope. The top of ladder touches the wall at 9ft and the base of the ladder is at a distance of ,say x ft.
Here we get a right -angled triangle where base is x ft, the ladder forms the hypotenuse ,H and the wall is the height of the triangle.
Base= x ft
height,h= 9ft and Hypotenuse H=x+3 ft
here we will apply Pythagoras theorem
H^2=h^2+ b^2
(x+3)^2 = 9^2 + x^2
Apply the formula(a+b)^2= a^2 +b^2 +2ab
x^2 +3^2 +2*x*3 =81 + x^2
x^2 get cancelled on both the sides
9 +6x= 81
6x= 81-9
6x= 72
x=72/6= 12
Base is 12 ft
Lenght of the ladder= (x+3)ft= 12 +3= 15ft
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