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

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