Question 181933
Let x=length of ladder



Since "the distance from the ground to the top of the ladder in one foot less than the length of the ladder.", this means that one leg of the triangle is {{{x-1}}} ft. Also, we're given the other leg of 5 ft.



So this tells us that {{{a=5}}}, {{{b=x-1}}} and {{{c=x}}}



{{{a^2+b^2=c^2}}} Start with Pythagorean's Theorem



{{{5^2+(x-1)^2=x^2}}} Plug in {{{a=5}}}, {{{b=x-1}}} and {{{c=x}}}



{{{25+(x-1)^2=x^2}}} Square 5 to get 25



{{{25+x^2-2x+1=x^2}}} FOIL



{{{25+x^2-2x+1-x^2=0}}} Subtract {{{x^2}}} from both sides.



{{{-2x+26=0}}} Combine like terms.



{{{-2x=0-26}}} Subtract {{{26}}} from both sides.



{{{-2x=-26}}} Combine like terms on the right side.



{{{x=(-26)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{x}}}.



{{{x=13}}} Reduce.



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Answer:


So the answer is {{{x=13}}}



So this means that the length of the ladder is 13 ft while the height that the ladder reaches on the building is 12 ft.