SOLUTION: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 10 feet. Find the distance from the wall to the bottom of the ladder if the length of the

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Question 754465: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 10 feet. Find the distance from the wall to the bottom of the ladder if the length of the ladder is two feet more than its distance from the wall.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
A ladder is resting against a wall making a shape of right angle triangle:
the ladder- hypotenuse c
the distance from the wall and the distance from the top of the ladder to the ground are legs a and b
if the distance from the top of the ladder to the ground is b=10ft
if the length of the ladder is two feet more than its distance from the wall, then we have c=a%2B2ft
c%5E2=a%5E2%2Bb%5E2
%28a%2B2ft%29%5E2=a%5E2%2B%2810ft%29%5E2
a%5E2%2B4aft%2B4ft%5E2=a%5E2%2B100ft%5E2
cross%28a%5E2%29%2B4aft%2B4ft%5E2=cross%28a%5E2%29%2B100ft%5E2
4aft%2B4ft%5E2=100ft%5E2
cross%284%291across%28ft%29=cross%28100%2925ft%5Ecross%282%29-cross%284%291ft%5Ecross%282%29
a=25ft-1ft
highlight%28a=24ft%29......the distance from the wall to the bottom of the ladder
now find c=a%2B2ft
c=24ft%2B2ft
highlight%28c=26ft%29.....the length of the ladder
check:
c%5E2=a%5E2%2Bb%5E2
%2826ft%29%5E2=%2824ft%29%5E2%2B%2810ft%29%5E2
676ft%5E2=576ft%5E2%2B100ft%5E2
676ft%5E2=676ft%5E2