The height of a triangle is 6 feet greater than the base the area of the triangle is 108 square feet find the length of the base and the height of the triangle

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