Find the Area of Triangle ABC

Question

Another question on my daily test, I suspect that is there is a theory that I haven't learn or the question doesn't have an answer. Try solving it :)

Triangle ABC is divided into 6 small triangles. The area of the small triangles are listed. What is the area of triangle ABC?

A.) 53

B.) 56

C.) 63

D.) 68

E.) 73

Answer 1

Hint:

Making use of the fact that bases of the triangles are same, we can solve any two of the following ratios to find $x$ and $y$ : $$\frac{8}{6}=\frac{16.8+x+8}{y+7+6}$$ $$\frac{7}{y}=\frac{8+6+7}{x+16.8+y}$$ $$\frac{16.8}{x}=\frac{7+y+16.8}{x+8+6}$$

Note: If the third equation doesn't satisfy the values derived from any two equations, then such a triangle does not exists.