He height of a triangle is 9 m less than is base the area is 56 m^2 what is the length of the base?

Formula for area of triangle:

A = 1/2 bh

Where b is the base and h is the height of the triangle.

Here, h = b-9

A=56 m^2

Put values in formula.

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

56=b (b-9) / 2

Multiply both sides by 2.

112=b^2-9b

or

b^2-9b-112=0

Factorise the equation.

b^2-16b+7b-112=0

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

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

Using zero factor theorem.

b+7=0 or b=-7

and

b-16=0 or b=16

Ignore the value b=-7, because length cannot be negative.

So length of base=16 m

Answer: Base=16m