Area of Triangle inside a Rectangle

Question

Rectangle $WXYZ$ has an area of $25$. Point $U\ \&\ V$ lie at the sides $XY\ \&\ YZ$,respectively$. $$\triangle WXU$ has an area of $6$ & $\triangle WZV$ has an area of $5$. Find the area of $\triangle WUV$.

So I decided to draw a diagram to see how it looked & I can't seemed to figure out the area. I got four triangles inside the rectangle where two of them already has an area. Can anybody give me a hint on how should I solve this?

Answer 1

Let $XW=a$ and $ZW=b$.

Thus, $ab=25$ and $$S_{\Delta WUV}=25-6-5-\frac{1}{2}\left(a-\frac{10}{b}\right)\left(b-\frac{12}{a}\right).$$ Can you end it now?

I got $$S_{\Delta WUV}=10.1.$$