Question 1071473
The 6 unit side on the bottom, horizontally
Drawn altitude;
Left right triangle altitude y, hyptoenuse 5, leg 6-x;
Right right triangle, altitude y, hypotenuse 4, leg x;


Left and Right triangles give  {{{system((6-x)^2+y^2=25,x^2+y^2=16)}}}


Finding y^2 from both equations and equating:
{{{25-(6-x)^2=16-x^2}}}
solving for x gives {{{x=9/4}}}.


Using x=9/4 in y^2+x^2=16,
.
{{{y^2+(9/4)^2=16}}}
.
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{{{highlight(y=(5/4)sqrt(7))}}}-------the altitude.