Question 1069100
Let's have the length of the height be "h". 
The base exceeds the height (h) by 4 feet: h + 4
The area of the triangle is 58.5 square feet. 

Area of triangle = (b x h) / 2
58.5 square feet = ((h + 4)(h))/2

Solve for h 
{{{((h+4)(h))/2 = 58.5 square feet}}}
{{{(h^2 + 4h) / 2 = 58.5}}}
{{{2((h^2 + 4h) / 2) = 2(58.5)}}}
{{{2h^2 + 8h = 117}}}
{{{2h^2 + 8h - 117 = 0}}}
{{{h = 5 sqrt(5/2) - 2}}}

So base = {{{4 + (5 sqrt(5/2) - 2)}}} and height = {{{5 sqrt(5/2) - 2}}}