To solve this problem, determine the $\theta$ angle for each diagonal and then compute the normal strains from the above strain transformation equations.

The normal strain ${\epsilon }_n$ acting at an arbitrary orientation $\theta$ is given by the strain transformation equation:

${\epsilon }_n={\epsilon }_x{\cos }^2\theta +{\epsilon }_y{\sin }^2\theta +{\gamma }_{xy}\sin \theta \cos \theta$

The equation can also be expressed in terms of double angle functions as:

${\epsilon }_n=\frac{{\epsilon }_x+{\epsilon }_y}{2}+\frac{{\displaystyle {\epsilon }_x-{\epsilon }_y}}{{\displaystyle 2}}\cos 2\theta +\frac{{\gamma }_{\mathrm{xy}}}{2}\sin 2\theta$

To use these equations, the following sign conventions are required:

1) Tensile strains are positive.

2) Shearing strains that decrease the angle between the two lines at the origin are positive.

3) Angles measured counterclockwise from the reference x-axis are positive.