The height of triangle is 8 meters less than its base. if the area of the triangle is 212.5 square meters, find the length of its bas and heiight.

If
b = length of base in meters, then
h = (b-8) m

Area of a triangle, A = (1/2)bh

Therefore,
212.5 = (1/2)(b)(b-8) = (1/2)(b^2-8b)
425 = b^2-8b
b^2 - 8b -425 =0
Solving the resulting quadratic equation;
b = [8+/- Sqrt [8^2 - 4(1)(-425)]]/2(1) = 4+/- 21 = 4+21 = 25 m (ignore negative value as it is not applicable)
Then,
h = b-8 = 25 - 8 = 17 m

Therefore,
Base = 25 m
Height = 17 m