Answer: the length of the base is 12 feet and the height is 18 feet.
Step-by-step explanation:
We would assume that the triangle is a right angle triangle. The formula for determining the area of a triangle is expressed as
Area = 1/2 × base × height
Let b represent the base of the triangle.
The height of the triangle is 6 feet greater than the base. It means that the height is (b + 6) feet.
If the area of the triangle is 108 square feet, it means that
108 = 1/2 × b(b + 6)
Cross multiplying by 2, it becomes
216 = b² + 6b
b² + 6b - 216 = 0
b² + 18b - 12b - 216 = 0
b(b + 18) - 12(b + 18) = 0
b - 12 = 0 or b + 18 = 0
b = 12 or b = - 18
Since the base cannot be negative, then b = 12 feet
Height = b + 6 = 12 + 6 = 18 feet
