Question 166039
Let x be the altitude, then the base is x + 9.
Its area is {{{(1/2)*x(x+9)}}}
As its area is 56, we have
{{{(1/2)*x(x+9)=56}}}
Solving for x, we have
{{{x(x+9)=112}}}
{{{x^2+9x=112}}}
{{{x^2+9x-112=0}}}
{{{x = (-9 +- sqrt( 9^2-4*1*(-112) ))/(2*1) }}}
{{{x = (-9 +- sqrt( 529 ))/2 }}}
{{{x = (-9 +- 23)/2 }}}
So
{{{x = (-9 + 23)/2=7 }}}
Or
{{{x = (-9 - 23)/2=-16}}} (reject this negative root)
Thus the length of the altitude is 7, and the length of the base is x+9 = 7+9=16.