Question 481965


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(-0.2,1.5,8),
locate(1,-0.2,6),
locate(1,2,x)
)}}}



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 {{{8}}} and {{{6}}} this means that {{{a=8}}} and {{{b=6}}}


   

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



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



{{{8^2+6^2=x^2}}} Plug in {{{a=8}}}, {{{b=6}}}, {{{c=x}}} 



{{{64+6^2=x^2}}} Square {{{8}}} to get {{{64}}}.



{{{64+36=x^2}}} Square {{{6}}} to get {{{36}}}.



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



{{{x^2=100}}} Rearrange the equation.



{{{x=sqrt(100)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



{{{x=10}}} Simplify the square root.



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Answer:



So the solution is {{{x=10}}}.



So the length of the diagonal is 10 cm.