$\dfrac{73}{75}$
$\dfrac{25}{27}$
$\dfrac{26}{27}$
$\dfrac{145}{147}$
$\dfrac{74}{75}$

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

Let the right angle be the origin

The hypotenuse is equated by 3x+4y=12.

Let the closest corner of S be (s,s).

The required distance is $\frac{3s+4s-12}{\sqrt{3^2+4^2}}=-2 \Rightarrow s=\frac{2}{7}$

note we use -2 as the distance because the point is under the line.

It then follows the area of the triangle is 6, the area of S is $\frac{4}{49}$ .

Thus the required fraction is $\frac{6-\frac{4}{49}}{6}=\frac{145}{147}$