Simple problem on an area of a triangle

Add two altitudes towards the bases of both triangles (big and small), one H from the top of the big triangle onto a side of 8+4=12 length and another h from the top of the small triangle onto a side of 8 length.
Let the unknown area of a small triangle be x.
Then
(a) 12·H = x + 36
(b) 8·h = x
(c) H/h = (8+3)/3
This is a simple system of three equations with three unknowns.
Divide the first equation (a) by the second (b):
(12·H)/(8·h) = (x + 36)/x
or
(d) (3/2)·(H/h) = 1 + 36/x
Using the third equation (c) that states that H/h = 11/3, express (d) as
(3/2)·(11/3) = 1 + 36/x
or
11/2 = 1 + 36/x
or
9/2 = 36/x
from which
x = 8