
Strength,
$S = bd^2$
Where:
$b = D \cos \theta$
$d = D \sin \theta$
$S = D^3 \cos \theta \sin^2 \theta$
$S = D^3 \cos \theta (1 - \cos^2 \theta)$
$S = D^3 (\cos \theta - \cos^3 \theta)$
$\dfrac{dS}{d\theta} = D^3 (-\sin \theta + 3\cos^2 \theta \sin \theta) = 0$
$-1 + 3\cos^2 \theta = 0$
$\cos^2 \theta = \frac{1}{3}$
$\cos \theta = \frac{1}{\sqrt{3}}$
$b = D \cos \theta = \frac{1}{\sqrt{3}}D$
$d = D \sin \theta = \dfrac{1}{\sqrt{3}} \sqrt{2} \, D$
$\text{depth } = \sqrt{2} \times \text{ breadth}$ answer