Question 172988
Let x=the distance from the bottom of the ladder to the building.





We basically have this triangle set up:



{{{drawing(500,500,-0.5,2,-0.5,3.2,
line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,24),
locate(1,-0.2,x),
locate(1,2,25)
)}}}



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^2+b^2=c^2}}} Start with the Pythagorean theorem.



{{{24^2+x^2=25^2}}} Plug in {{{a=24}}}, {{{b=x}}}, {{{c=25}}} 



{{{576+x^2=25^2}}} Square {{{24}}} to get {{{576}}}.



{{{576+x^2=625}}} Square {{{25}}} to get {{{625}}}.



{{{x^2=625-576}}} Subtract {{{576}}} from both sides.



{{{x^2=49}}} Combine like terms.



{{{x=sqrt(49)}}} 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.