A triangle has an area of 36 square feet. If the height of the triangle is 6 more feet than its base, what is its height and base?

If b is the base then the height h=b+6. As we have S=bh/2 then

36=b (b+6) / 2;

b²+6b-72=0;

D/4=3²+72=81

b₁=-3-9=-12

b₂=-3+9=6.

The base is always positive so b=6, h=6+6=12.

Answer: base=6 ft, height=12 ft.