The height of a triangle is 9 m less than its base. the area of the triangle is 56 m2. find the length of the base.

Let the base be b.
The height is b - 9.

Area of triangle = 1/2 x base x height
56 m² = 1/2 x b x (b - 9)

56 = -1/2b(b - 9)

112 = b² - 9b

b² - 9b - 112 = 0

(b + 7)(b - 16) = 0

b = - 7 (rejected, b cannot be negative) or b = 16

The base is 16 m