Question 138181
The area of a triangle is {{{A=(1/2)bh}}} where b is the base and h is the height or altitude.  The base is that side of the triangle to which the altitude is drawn.


So, if x is the altitude then 3x is the base because the length of the altitute is one third the length of the base.


Substituting in the area formula:  {{{(1/2)(3x)(x)=6}}}


{{{(1/2)3x^2=6}}}


{{{(1/2)x^2=2}}}


{{{x^2=4}}}


{{{x=sqrt(4)=2}}} (ignore the negative square root because we are calculating a length)


So, the altitude is {{{2}}}.


Check the answer:


{{{A=(1/2)bh}}}


{{{b=3h=3*2=6}}}, so


{{{A=(1/2)(6)(2)=6}}} Answer checks.