Rhombus Diagonals Difference

Let $d_1$ and $d_2$ be the lengths of the diagonals of the rhombus. Area of rhombus $= \frac{1}{2} d_1 d_2 = 396 \implies d_1 d_2 = 792$. Side $a = 36 \implies \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 = a^2 = 36^2 = 1296$. $d_1^2 + d_2^2 = 4 \times 1296 = 5184$ We need $|d_1 - d_2|$: $(d_1 - d_2)^2 = d_1^2 + d_2^2 - 2 d_1 d_2 = 5184 - 2(792) = 5184 - 1584 = 3600$ $|d_1 - d_2| = \sqrt{3600} = 60$ Thus, the difference between the diagonal lengths is 60 cm.