SOLUTION: a ladder is 25ft long. the ladder needs to reach to a window that is 24ft above the ground.how far awayfrom the building should the bottom of the ladder be placed?

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Question 172988This question is from textbook algebra 1
: a ladder is 25ft long. the ladder needs to reach to a window that is 24ft above the ground.how far awayfrom the building should the bottom of the ladder be placed? This question is from textbook algebra 1

Found 3 solutions by jim_thompson5910, Mathtut, monika_p:
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Let x=the distance from the bottom of the ladder to the building.




We basically have this triangle set up:





Since the legs are 24 and x this means that a=24 and b=x


Also, since the hypotenuse is 25, this means that c=25.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


24%5E2%2Bx%5E2=25%5E2 Plug in a=24, b=x, c=25


576%2Bx%5E2=25%5E2 Square 24 to get 576.


576%2Bx%5E2=625 Square 25 to get 625.


x%5E2=625-576 Subtract 576 from both sides.


x%5E2=49 Combine like terms.


x=sqrt%2849%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=7 Simplify the square root.


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Answer:


So the solution is x=7.


This means that the bottom of the ladder should be placed 7 ft from the building.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
pathagorean theorem:
:
24%5E2%2Bx%5E2=25%5E2
:
675%2Bx%5E2=625
:
x%5E2=49
:
highlight%28x=7%29feet
x=-7 was thrown out because you cant have negative length

Answer by monika_p(71) About Me  (Show Source):
You can put this solution on YOUR website!
The ladder will make a right triangle with wall of the building and ground. The right angle will be between wall and ground and ladder will be hypotenuse of the triangle.Lets ladder will have lenght x=25, wall y=24 and distance on the ground z, which we have to find. To find lenght z use Pythagorean Theorem
y^2+z^2=x^2
24^2+z^2=25^2
z^2= 625-576
z^2=49
z=7
Answer: The bottom of the ladder should be placed 7ft away from building