Question 146493
Let x=length of the lower part


If you draw the triangle, you'll get 


{{{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,x),
locate(1,-0.2,15),
locate(1,2,x+9)
)}}}



So we can use Pythagoreans theorem:


{{{a^2+b^2=c^2}}} where a and b are the legs of the triangle and c is the hypotenuse



{{{x^2+15^2=(x+9)^2}}} Plug in {{{a=x}}}, {{{b=15}}} and {{{c=x+9}}}



{{{x^2+225=(x+9)^2}}} Square 15 to get 225



{{{x^2+225=x^2+18x+81}}} FOIL



{{{x^2+225-x^2-18x-81=0}}} Get all terms to the left side.



{{{-18x+144=0}}} Combine like terms.




{{{-18x=0-144}}} Subtract {{{144}}} from both sides.



{{{-18x=-144}}} Combine like terms on the right side.



{{{x=(-144)/(-18)}}} Divide both sides by {{{-18}}} to isolate {{{x}}}.



{{{x=8}}} Reduce.


So the length of the lower part is 8 feet. Now let's find the length of the upper part:



{{{x+9}}} Start with the expression for length of the upper part



{{{8+9}}} Plug in {{{x=8}}}



{{{17}}}



So the length of the upper part is 17 feet



This means that the total length is {{{8+17=25}}} feet