Question 251800


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(-0.2,1.5,12),
locate(1,-0.2,10),
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 {{{12}}} and {{{10}}} this means that {{{a=12}}} and {{{b=10}}}


   

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



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



{{{12^2+10^2=x^2}}} Plug in {{{a=12}}}, {{{b=10}}}, {{{c=x}}} 



{{{144+10^2=x^2}}} Square {{{12}}} to get {{{144}}}.



{{{144+100=x^2}}} Square {{{10}}} to get {{{100}}}.



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



{{{x^2=244}}} Rearrange the equation.



{{{x=sqrt(244)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



{{{x=2*sqrt(61)}}} Simplify the square root.



{{{x=15.6205}}} Approximate the right side with a calculator.



================================================================



Answer:



So the solution is approximately {{{x=15.6205}}} which means that the hypotenuse is roughly 15.6 (rounded to the nearest tenth) units long.