Question: Find all natural numbers $a$ and $b$ such that $\gcd(a,b)=1$ and 
$$\dfrac{a}{b}=b.a$$
 Also $b.a$ is a decimal number.

For example $\dfrac{5}{2}=2.5$

Answer: 
This problem can be solved with similar triangles property.

The White triangle is similar to the Red one
Now Ratio of sides is $2:3$ (as the ratio of areas = ratio of bases if the height is same)

Seeking that, area of the white triangle $= \frac{9}{4} \times$ area of the red triangle $= \frac{9}{2}$
Following all the above, the Green region = $5.5$ units
This problem can be solved with similar triangles property.