Question 252631


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,x),
locate(1,-0.2,16),
locate(1,2,20)
)}}}



To find the unknown length, we need to use the Pythagorean Theorem.



Remember, the Pythagorean Theorem is {{{a^2+b^2=c^2}}} where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.



Since the legs are {{{x}}} and {{{16}}} this means that {{{a=x}}} and {{{b=16}}}


   

Also, since the hypotenuse is {{{20}}}, this means that {{{c=20}}}.



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



{{{x^2+16^2=20^2}}} Plug in {{{a=x}}}, {{{b=16}}}, {{{c=20}}} 



{{{x^2+256=20^2}}} Square {{{16}}} to get {{{256}}}.



{{{x^2+256=400}}} Square {{{20}}} to get {{{400}}}.



{{{x^2=400-256}}} Subtract {{{256}}} from both sides.



{{{x^2=144}}} Combine like terms.



{{{x=sqrt(144)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



{{{x=12}}} Simplify the square root.



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Answer:



So the solution is {{{x=12}}} which means that the measure of the remaining leg is 12 inches.