Metal Beam Breaking Gain or Loss

Let the lengths of the two broken pieces be $4x$ and $9x$. The original length of the beam was $4x + 9x = 13x$.

The market value $V$ is proportional to $L^2$, so $V = k L^2$. Original Value = $k(13x)^2 = 169 k x^2$. New Value = $k(4x)^2 + k(9x)^2 = 16 k x^2 + 81 k x^2 = 97 k x^2$.

Loss = $169 k x^2 - 97 k x^2 = 72 k x^2$. Percentage Loss = $\frac{72 k x^2}{169 k x^2} \times 100\% \approx 42.60\%$.