The trick in this problem is realizing that when the two triangles share the same height, the ratio of the two bases equals to the ratio of the two areas.

Now obviously the area of

hence,

Therefore,

Similarly,

Now assign the follow variables to the area of the following triangles,

note that,

then we have,

and

Solving this system of equations yields,

Similarly,

and

Solving the system we get,

Finally,

Therefore the area of triangle PQU is

Advertisements