Question 150635
Let x=length of first leg and y=length of second leg



Since the "length of a leg of a right triangle is two times the length of the other", this means that {{{y=2x}}}. So in this case "y" is the longer leg.



So with the use of Pythagoreans theorem, we get


{{{x^2+y^2=25^2}}}



{{{x^2+y^2=625}}} Square 25 to get 625



{{{x^2+(2x)^2=625}}} Plug in {{{y=2x}}}



{{{x^2+4x^2=625}}} Square {{{2x}}} to get {{{4x^2}}}



{{{5x^2=625}}} Add



{{{x^2=125}}} Divide both sides by 5.



{{{x=sqrt(125)}}} Take the square root of both sides. Note: only the positive square root is considered.



{{{x=5*sqrt(5)}}} Simplify the square root.




So the length of one leg is {{{x=5*sqrt(5)}}} (which approximates to {{{x=11.18}}}) and the length of the longer leg is {{{y=2*5*sqrt(5)=10*sqrt(5)}}} (which approximates to {{{y=22.36}}})