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