The base of a triangle exceeds the height by 9 feet. if the area is 180 square feet, find the length of the base and the height of the triangle.

Base = x + 9
height = x
Area = 1/2 · b · h
  180 = 1/2 (x + 9)(x)
  180 = (x² + 9x)/2
   360 = x² + 9x
     0  = x² + 9x - 360

Use Quadratic Formula to solve:
x = (-b +/- √b² - 4ac)/(2a)
  = (-9 +/- √9² - 4·1·-360)/(2·1)
  = (-9 +/- √9² + 1440)/(2)
  = (-9 +/- √1449)/(2)
  = (-9 +/- 38)/(2)
  = (-9 + 38)/(2) , (-9 - 38)/(2)
  =        29/2      ,      -47/2
  =        14.5      ,        -23.5
length cannot be negative!!! so disregard the -23.5

The height of the triangle is 14.5 ft and the base is 14.5 + 9 = 23.5 ft

No a triangle cannot be formed because when you add the two smallest number together (which would be 11) the have to be bigger than the number it is "against" ( which would be 12)