Question 176435
If we cut the rectangle in half along the diagonal, we get the following triangle:


{{{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,-0.2,30),
locate(1,2,34)
)}}}



Since the legs are {{{x}}} and {{{30}}} this means that {{{a=x}}} and {{{b=30}}}


   

Also, since the hypotenuse is {{{34}}}, this means that {{{c=34}}}.



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



{{{x^2+30^2=34^2}}} Plug in {{{a=x}}}, {{{b=30}}}, {{{c=34}}} 



{{{x^2+900=34^2}}} Square {{{30}}} to get {{{900}}}.



{{{x^2+900=1156}}} Square {{{34}}} to get {{{1156}}}.



{{{x^2=1156-900}}} Subtract {{{900}}} from both sides.



{{{x^2=256}}} Combine like terms.



{{{x=sqrt(256)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



{{{x=16}}} Simplify the square root.



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Answer:



So the solution is {{{x=16}}} which means that the other side length is 16 mm