Question 180768
Since there's a hypotenuse, this means that the triangle must be a right triangle. 



So 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,x),
locate(1,2,15)
)}}}



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


   

Also, since the hypotenuse is {{{15}}}, this means that {{{c=15}}}.



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



{{{x^2+x^2=15^2}}} Plug in {{{a=x}}}, {{{b=x}}}, {{{c=15}}} 



{{{x^2+x^2=225}}} Square {{{15}}} to get {{{225}}}.



{{{2x^2=225}}} Combine like terms.



{{{x^2=225/2}}} Divide both sides by 2.



{{{x=sqrt(225/2)}}} Take the square root of both sides. Note: we're only dealing with the positive square root.



{{{x=(15*sqrt(2))/2}}} Simplify the square root.



{{{x=10.61}}} Approximate



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Answer:



So the solution is approximately {{{x=10.61}}} which means that the length of the two equal sides is about 10.61 cm