Question 592875


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(-0.2,1.5,5),
locate(1,-0.2,7),
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 {{{5}}} and {{{7}}} this means that {{{a=5}}} and {{{b=7}}}


   

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



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



{{{5^2+7^2=x^2}}} Plug in {{{a=5}}}, {{{b=7}}}, {{{c=x}}} 



{{{25+7^2=x^2}}} Square {{{5}}} to get {{{25}}}.



{{{25+49=x^2}}} Square {{{7}}} to get {{{49}}}.



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



{{{x^2=74}}} Rearrange the equation.



{{{x=sqrt(74)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



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Answer:



So the solution is {{{x=sqrt(74)}}} which approximates to {{{x=8.602}}}.



So the hypotenuse is roughly 8.602 units long.